Solve -4 2z^2 - 5z 8 z^2 9z

Question

Simplify the expression

- 42 z^{2} - 360 z^{4}

Evaluate

- 42 z^{2} - 5 z \times 8 z^{2} \times 9 z

Solution

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Evaluate

5 z \times 8 z^{2} \times 9 z

Multiply the terms

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Evaluate

5 \times 8 \times 9

Multiply the terms

40 \times 9

Multiply the numbers

360

360 z \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

360 z^{1 + 2 + 1}

Add the numbers

360 z^{4}

- 42 z^{2} - 360 z^{4}

Show Solution

Factor the expression

- 6 z^{2} (7 + 60 z^{2})

Evaluate

- 42 z^{2} - 5 z \times 8 z^{2} \times 9 z

Multiply

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Evaluate

5 z \times 8 z^{2} \times 9 z

Multiply the terms

More Steps

Evaluate

5 \times 8 \times 9

Multiply the terms

40 \times 9

Multiply the numbers

360

360 z \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

360 z^{1 + 2 + 1}

Add the numbers

360 z^{4}

- 42 z^{2} - 360 z^{4}

Rewrite the expression

- 6 z^{2} \times 7 - 6 z^{2} \times 60 z^{2}

Solution

- 6 z^{2} (7 + 60 z^{2})

Show Solution

Find the roots

z_{1} = - \frac{105}{30} i, z_{2} = \frac{105}{30} i, z_{3} = 0

Alternative Form

z_{1} \approx - 0.341565 i, z_{2} \approx 0.341565 i, z_{3} = 0

Evaluate

- 42 z^{2} - 5 z \times 8 z^{2} \times 9 z

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

- 42 z^{2} - 5 z \times 8 z^{2} \times 9 z = 0

Multiply

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Multiply the terms

5 z \times 8 z^{2} \times 9 z

Multiply the terms

More Steps

Evaluate

5 \times 8 \times 9

Multiply the terms

40 \times 9

Multiply the numbers

360

360 z \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

360 z^{1 + 2 + 1}

Add the numbers

360 z^{4}

- 42 z^{2} - 360 z^{4} = 0

Factor the expression

- 6 z^{2} (7 + 60 z^{2}) = 0

Divide both sides

z^{2} (7 + 60 z^{2}) = 0

Separate the equation into 2 possible cases

z^{2} = 0 7 + 60 z^{2} = 0

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

z = 0 7 + 60 z^{2} = 0

Solve the equation

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Evaluate

7 + 60 z^{2} = 0

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

60 z^{2} = 0 - 7

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

60 z^{2} = - 7

Divide both sides

\frac{60 z ^{2}}{60} = \frac{- 7}{60}

Divide the numbers

z^{2} = \frac{- 7}{60}

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

z^{2} = - \frac{7}{60}

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

z = \pm - \frac{7}{60}

Simplify the expression

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Evaluate

- \frac{7}{60}

Evaluate the power

\frac{7}{60} \times - 1

Evaluate the power

\frac{7}{60} \times i

Evaluate the power

\frac{105}{30} i

z = \pm \frac{105}{30} i

Separate the equation into 2 possible cases

z = \frac{105}{30} i z = - \frac{105}{30} i

z = 0 z = \frac{105}{30} i z = - \frac{105}{30} i

Solution

z_{1} = - \frac{105}{30} i, z_{2} = \frac{105}{30} i, z_{3} = 0

Alternative Form

z_{1} \approx - 0.341565 i, z_{2} \approx 0.341565 i, z_{3} = 0

Show Solution