Solve (-5x^46x^3-43) (6x^5-x^212x 12)

Question

Simplify the expression

- 180 x^{12} + 4320 x^{10} - 258 x^{5} + 6192 x^{3}

Evaluate

(- 5 x^{4} \times 6 x^{3} - 43) (6 x^{5} - x^{2} \times 12 x \times 12)

Multiply

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Multiply the terms

- 5 x^{4} \times 6 x^{3}

Multiply the terms

- 30 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

- 30 x^{4 + 3}

Add the numbers

- 30 x^{7}

(- 30 x^{7} - 43) (6 x^{5} - x^{2} \times 12 x \times 12)

Multiply

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Multiply the terms

x^{2} \times 12 x \times 12

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12 \times 12

Add the numbers

x^{3} \times 12 \times 12

Multiply the terms

x^{3} \times 144

Use the commutative property to reorder the terms

144 x^{3}

(- 30 x^{7} - 43) (6 x^{5} - 144 x^{3})

Apply the distributive property

- 30 x^{7} \times 6 x^{5} - (- 30 x^{7} \times 144 x^{3}) - 43 \times 6 x^{5} - (- 43 \times 144 x^{3})

Multiply the terms

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Evaluate

- 30 x^{7} \times 6 x^{5}

Multiply the numbers

- 180 x^{7} \times x^{5}

Multiply the terms

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Evaluate

x^{7} \times x^{5}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{7 + 5}

Add the numbers

x^{12}

- 180 x^{12}

- 180 x^{12} - (- 30 x^{7} \times 144 x^{3}) - 43 \times 6 x^{5} - (- 43 \times 144 x^{3})

Multiply the terms

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Evaluate

- 30 x^{7} \times 144 x^{3}

Multiply the numbers

- 4320 x^{7} \times x^{3}

Multiply the terms

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Evaluate

x^{7} \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{7 + 3}

Add the numbers

x^{10}

- 4320 x^{10}

- 180 x^{12} - (- 4320 x^{10}) - 43 \times 6 x^{5} - (- 43 \times 144 x^{3})

Multiply the numbers

- 180 x^{12} - (- 4320 x^{10}) - 258 x^{5} - (- 43 \times 144 x^{3})

Multiply the numbers

- 180 x^{12} - (- 4320 x^{10}) - 258 x^{5} - (- 6192 x^{3})

Solution

- 180 x^{12} + 4320 x^{10} - 258 x^{5} + 6192 x^{3}

Show Solution

Factor the expression

- 6 x^{3} (30 x^{7} + 43) (x^{2} - 24)

Evaluate

(- 5 x^{4} \times 6 x^{3} - 43) (6 x^{5} - x^{2} \times 12 x \times 12)

Multiply

More Steps

Multiply the terms

- 5 x^{4} \times 6 x^{3}

Multiply the terms

- 30 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

- 30 x^{4 + 3}

Add the numbers

- 30 x^{7}

(- 30 x^{7} - 43) (6 x^{5} - x^{2} \times 12 x \times 12)

Multiply

More Steps

Multiply the terms

x^{2} \times 12 x \times 12

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12 \times 12

Add the numbers

x^{3} \times 12 \times 12

Multiply the terms

x^{3} \times 144

Use the commutative property to reorder the terms

144 x^{3}

(- 30 x^{7} - 43) (6 x^{5} - 144 x^{3})

Factor the expression

- (30 x^{7} + 43) (6 x^{5} - 144 x^{3})

Factor the expression

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Evaluate

6 x^{5} - 144 x^{3}

Rewrite the expression

6 x^{3} \times x^{2} - 6 x^{3} \times 24

Factor out 6 x^{3} from the expression

6 x^{3} (x^{2} - 24)

- (30 x^{7} + 43) \times 6 x^{3} (x^{2} - 24)

Solution

- 6 x^{3} (30 x^{7} + 43) (x^{2} - 24)

Show Solution

Find the roots

x_{1} = - 26, x_{2} = - \frac{7 43 \times 3 0 ^{6}}{30}, x_{3} = 0, x_{4} = 26

Alternative Form

x_{1} \approx - 4.898979, x_{2} \approx - 1.052774, x_{3} = 0, x_{4} \approx 4.898979

Evaluate

(- 5 x^{4} \times 6 x^{3} - 43) (6 x^{5} - x^{2} \times 12 x \times 12)

To find the roots of the expression,set the expression equal to 0

(- 5 x^{4} \times 6 x^{3} - 43) (6 x^{5} - x^{2} \times 12 x \times 12) = 0

Multiply

More Steps

Multiply the terms

- 5 x^{4} \times 6 x^{3}

Multiply the terms

- 30 x^{4} \times x^{3}

Multiply the terms with the same base by adding their exponents

- 30 x^{4 + 3}

Add the numbers

- 30 x^{7}

(- 30 x^{7} - 43) (6 x^{5} - x^{2} \times 12 x \times 12) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 12 x \times 12

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 12 \times 12

Add the numbers

x^{3} \times 12 \times 12

Multiply the terms

x^{3} \times 144

Use the commutative property to reorder the terms

144 x^{3}

(- 30 x^{7} - 43) (6 x^{5} - 144 x^{3}) = 0

Change the sign

(30 x^{7} + 43) (6 x^{5} - 144 x^{3}) = 0

Separate the equation into 2 possible cases

30 x^{7} + 43 = 0 6 x^{5} - 144 x^{3} = 0

Solve the equation

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Evaluate

30 x^{7} + 43 = 0

Move the constant to the right-hand side and change its sign

30 x^{7} = 0 - 43

Removing 0 doesn't change the value,so remove it from the expression

30 x^{7} = - 43

Divide both sides

\frac{30 x ^{7}}{30} = \frac{- 43}{30}

Divide the numbers

x^{7} = \frac{- 43}{30}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{7} = - \frac{43}{30}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 - \frac{43}{30}

Calculate

x = 7 - \frac{43}{30}

Simplify the root

More Steps

Evaluate

7 - \frac{43}{30}

An odd root of a negative radicand is always a negative

- 7 \frac{43}{30}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{7 43}{7 30}

Multiply by the Conjugate

\frac{- 7 43 \times 7 3 0 ^{6}}{7 30 \times 7 3 0 ^{6}}

The product of roots with the same index is equal to the root of the product

\frac{- 7 43 \times 3 0 ^{6}}{7 30 \times 7 3 0 ^{6}}

Multiply the numbers

\frac{- 7 43 \times 3 0 ^{6}}{30}

Calculate

- \frac{7 43 \times 3 0 ^{6}}{30}

x = - \frac{7 43 \times 3 0 ^{6}}{30}

x = - \frac{7 43 \times 3 0 ^{6}}{30} 6 x^{5} - 144 x^{3} = 0

Solve the equation

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Evaluate

6 x^{5} - 144 x^{3} = 0

Factor the expression

6 x^{3} (x^{2} - 24) = 0

Divide both sides

x^{3} (x^{2} - 24) = 0

Separate the equation into 2 possible cases

x^{3} = 0 x^{2} - 24 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{2} - 24 = 0

Solve the equation

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Evaluate

x^{2} - 24 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 24

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 24

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 24

Simplify the expression

x = \pm 26

Separate the equation into 2 possible cases

x = 26 x = - 26

x = 0 x = 26 x = - 26

x = - \frac{7 43 \times 3 0 ^{6}}{30} x = 0 x = 26 x = - 26

Solution

x_{1} = - 26, x_{2} = - \frac{7 43 \times 3 0 ^{6}}{30}, x_{3} = 0, x_{4} = 26

Alternative Form

x_{1} \approx - 4.898979, x_{2} \approx - 1.052774, x_{3} = 0, x_{4} \approx 4.898979

Show Solution