Solve (x^2 6x -5) (2x^2 15)

Question

Simplify the expression

180 x^{5} - 150 x^{2}

Evaluate

(x^{2} \times 6 x - 5) (2 x^{2} \times 15)

Remove the parentheses

(x^{2} \times 6 x - 5) \times 2 x^{2} \times 15

Multiply

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Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

(6 x^{3} - 5) \times 2 x^{2} \times 15

Multiply the terms

(6 x^{3} - 5) \times 30 x^{2}

Multiply the terms

30 x^{2} (6 x^{3} - 5)

Apply the distributive property

30 x^{2} \times 6 x^{3} - 30 x^{2} \times 5

Multiply the terms

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Evaluate

30 x^{2} \times 6 x^{3}

Multiply the numbers

180 x^{2} \times x^{3}

Multiply the terms

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Evaluate

x^{2} \times x^{3}

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

x^{2 + 3}

Add the numbers

x^{5}

180 x^{5}

180 x^{5} - 30 x^{2} \times 5

Solution

180 x^{5} - 150 x^{2}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 180}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.941036

Evaluate

(x^{2} \times 6 x - 5) (2 x^{2} \times 15)

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

(x^{2} \times 6 x - 5) (2 x^{2} \times 15) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

(6 x^{3} - 5) (2 x^{2} \times 15) = 0

Multiply the terms

(6 x^{3} - 5) \times 30 x^{2} = 0

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

x^{2} = 0 6 x^{3} - 5 = 0

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

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

Solve the equation

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Evaluate

6 x^{3} - 5 = 0

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

6 x^{3} = 0 + 5

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

6 x^{3} = 5

Divide both sides

\frac{6 x ^{3}}{6} = \frac{5}{6}

Divide the numbers

x^{3} = \frac{5}{6}

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

3 x^{3} = 3 \frac{5}{6}

Calculate

x = 3 \frac{5}{6}

Simplify the root

More Steps

Evaluate

3 \frac{5}{6}

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

\frac{3 5}{3 6}

Multiply by the Conjugate

\frac{3 5 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 5 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{6}

x = \frac{3 180}{6}

x = 0 x = \frac{3 180}{6}

Solution

x_{1} = 0, x_{2} = \frac{3 180}{6}

Alternative Form

x_{1} = 0, x_{2} \approx 0.941036

Show Solution