Solve 6(-6 -6h^(2)) 10(3h -8)

Question

Simplify the expression

- 1080 h + 2880 - 1080 h^{3} + 2880 h^{2}

Evaluate

6 (- 6 - 6 h^{2}) \times 10 (3 h - 8)

Multiply the terms

60 (- 6 - 6 h^{2}) (3 h - 8)

Multiply the terms

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Evaluate

60 (- 6 - 6 h^{2})

Apply the distributive property

60 (- 6) - 60 \times 6 h^{2}

Multiply the numbers

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Evaluate

60 (- 6)

Multiplying or dividing an odd number of negative terms equals a negative

- 60 \times 6

Multiply the numbers

- 360

- 360 - 60 \times 6 h^{2}

Multiply the numbers

- 360 - 360 h^{2}

(- 360 - 360 h^{2}) (3 h - 8)

Apply the distributive property

- 360 \times 3 h - (- 360 \times 8) - 360 h^{2} \times 3 h - (- 360 h^{2} \times 8)

Multiply the numbers

- 1080 h - (- 360 \times 8) - 360 h^{2} \times 3 h - (- 360 h^{2} \times 8)

Multiply the numbers

- 1080 h - (- 2880) - 360 h^{2} \times 3 h - (- 360 h^{2} \times 8)

Multiply the terms

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Evaluate

- 360 h^{2} \times 3 h

Multiply the numbers

- 1080 h^{2} \times h

Multiply the terms

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Evaluate

h^{2} \times h

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

h^{2 + 1}

Add the numbers

h^{3}

- 1080 h^{3}

- 1080 h - (- 2880) - 1080 h^{3} - (- 360 h^{2} \times 8)

Multiply the numbers

- 1080 h - (- 2880) - 1080 h^{3} - (- 2880 h^{2})

Solution

- 1080 h + 2880 - 1080 h^{3} + 2880 h^{2}

Show Solution

Factor the expression

- 360 (1 + h^{2}) (3 h - 8)

Evaluate

6 (- 6 - 6 h^{2}) \times 10 (3 h - 8)

Multiply the terms

60 (- 6 - 6 h^{2}) (3 h - 8)

Factor the expression

60 (- 6) (1 + h^{2}) (3 h - 8)

Solution

- 360 (1 + h^{2}) (3 h - 8)

Show Solution

Find the roots

h_{1} = \frac{8}{3}, h_{2} = - i, h_{3} = i

Alternative Form

h_{1} = 2. \dot{6}, h_{2} = - i, h_{3} = i

Evaluate

6 (- 6 - 6 h^{2}) \times 10 (3 h - 8)

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

6 (- 6 - 6 h^{2}) \times 10 (3 h - 8) = 0

Multiply the terms

60 (- 6 - 6 h^{2}) (3 h - 8) = 0

Elimination the left coefficient

(- 6 - 6 h^{2}) (3 h - 8) = 0

Separate the equation into 2 possible cases

- 6 - 6 h^{2} = 0 3 h - 8 = 0

Solve the equation

More Steps

Evaluate

- 6 - 6 h^{2} = 0

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

- 6 h^{2} = 0 + 6

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

- 6 h^{2} = 6

Change the signs on both sides of the equation

6 h^{2} = - 6

Divide both sides

\frac{6 h ^{2}}{6} = \frac{- 6}{6}

Divide the numbers

h^{2} = \frac{- 6}{6}

Divide the numbers

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Evaluate

\frac{- 6}{6}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

h^{2} = - 1

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

h = \pm - 1

Simplify the expression

h = \pm i

Separate the equation into 2 possible cases

h = i h = - i

h = i h = - i 3 h - 8 = 0

Solve the equation

More Steps

Evaluate

3 h - 8 = 0

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

3 h = 0 + 8

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

3 h = 8

Divide both sides

\frac{3 h}{3} = \frac{8}{3}

Divide the numbers

h = \frac{8}{3}

h = i h = - i h = \frac{8}{3}

Solution

h_{1} = \frac{8}{3}, h_{2} = - i, h_{3} = i

Alternative Form

h_{1} = 2. \dot{6}, h_{2} = - i, h_{3} = i

Show Solution