Solve (x-6)⋅(-3x^(2) 5x-2)

Question

Simplify the expression

- 15 x^{4} - 2 x + 90 x^{3} + 12

Evaluate

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

Multiply

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Evaluate

- 3 x^{2} \times 5 x

Multiply the terms

- 15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 15 x^{2 + 1}

Add the numbers

- 15 x^{3}

(x - 6) (- 15 x^{3} - 2)

Apply the distributive property

x (- 15 x^{3}) - x \times 2 - 6 (- 15 x^{3}) - (- 6 \times 2)

Multiply the terms

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Evaluate

x (- 15 x^{3})

Use the commutative property to reorder the terms

- 15 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

- 15 x^{4}

- 15 x^{4} - x \times 2 - 6 (- 15 x^{3}) - (- 6 \times 2)

Use the commutative property to reorder the terms

- 15 x^{4} - 2 x - 6 (- 15 x^{3}) - (- 6 \times 2)

Multiply the numbers

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Evaluate

- 6 (- 15)

Multiplying or dividing an even number of negative terms equals a positive

6 \times 15

Multiply the numbers

90

- 15 x^{4} - 2 x + 90 x^{3} - (- 6 \times 2)

Multiply the numbers

- 15 x^{4} - 2 x + 90 x^{3} - (- 12)

Solution

- 15 x^{4} - 2 x + 90 x^{3} + 12

Show Solution

Find the roots

x_{1} = - \frac{3 450}{15}, x_{2} = 6

Alternative Form

x_{1} \approx - 0.510873, x_{2} = 6

Evaluate

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

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

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

Multiply

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Multiply the terms

- 3 x^{2} \times 5 x

Multiply the terms

- 15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 15 x^{2 + 1}

Add the numbers

- 15 x^{3}

(x - 6) (- 15 x^{3} - 2) = 0

Separate the equation into 2 possible cases

x - 6 = 0 - 15 x^{3} - 2 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 - 15 x^{3} - 2 = 0

Solve the equation

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Evaluate

- 15 x^{3} - 2 = 0

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

- 15 x^{3} = 0 + 2

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

- 15 x^{3} = 2

Change the signs on both sides of the equation

15 x^{3} = - 2

Divide both sides

\frac{15 x ^{3}}{15} = \frac{- 2}{15}

Divide the numbers

x^{3} = \frac{- 2}{15}

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

x^{3} = - \frac{2}{15}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{2}{15}

Calculate

x = 3 - \frac{2}{15}

Simplify the root

More Steps

Evaluate

3 - \frac{2}{15}

An odd root of a negative radicand is always a negative

- 3 \frac{2}{15}

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

- \frac{3 2}{3 15}

Multiply by the Conjugate

\frac{- 3 2 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{- 3 2 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

\frac{- 3 450}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

\frac{- 3 450}{15}

Calculate

- \frac{3 450}{15}

x = - \frac{3 450}{15}

x = 6 x = - \frac{3 450}{15}

Solution

x_{1} = - \frac{3 450}{15}, x_{2} = 6

Alternative Form

x_{1} \approx - 0.510873, x_{2} = 6

Show Solution