Solve 4z^310z^2-24z

Question

Simplify the expression

40 z^{5} - 24 z

Evaluate

4 z^{3} \times 10 z^{2} - 24 z

Solution

More Steps

Evaluate

4 z^{3} \times 10 z^{2}

Multiply the terms

40 z^{3} \times z^{2}

Multiply the terms with the same base by adding their exponents

40 z^{3 + 2}

Add the numbers

40 z^{5}

40 z^{5} - 24 z

Show Solution

Factor the expression

8 z (5 z^{4} - 3)

Evaluate

4 z^{3} \times 10 z^{2} - 24 z

Multiply

More Steps

Evaluate

4 z^{3} \times 10 z^{2}

Multiply the terms

40 z^{3} \times z^{2}

Multiply the terms with the same base by adding their exponents

40 z^{3 + 2}

Add the numbers

40 z^{5}

40 z^{5} - 24 z

Rewrite the expression

8 z \times 5 z^{4} - 8 z \times 3

Solution

8 z (5 z^{4} - 3)

Show Solution

Find the roots

z_{1} = - \frac{4 375}{5}, z_{2} = 0, z_{3} = \frac{4 375}{5}

Alternative Form

z_{1} \approx - 0.880112, z_{2} = 0, z_{3} \approx 0.880112

Evaluate

4 z^{3} \times 10 z^{2} - 24 z

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

4 z^{3} \times 10 z^{2} - 24 z = 0

Multiply

More Steps

Multiply the terms

4 z^{3} \times 10 z^{2}

Multiply the terms

40 z^{3} \times z^{2}

Multiply the terms with the same base by adding their exponents

40 z^{3 + 2}

Add the numbers

40 z^{5}

40 z^{5} - 24 z = 0

Factor the expression

8 z (5 z^{4} - 3) = 0

Divide both sides

z (5 z^{4} - 3) = 0

Separate the equation into 2 possible cases

z = 0 5 z^{4} - 3 = 0

Solve the equation

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Evaluate

5 z^{4} - 3 = 0

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

5 z^{4} = 0 + 3

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

5 z^{4} = 3

Divide both sides

\frac{5 z ^{4}}{5} = \frac{3}{5}

Divide the numbers

z^{4} = \frac{3}{5}

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

z = \pm 4 \frac{3}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{5}

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

\frac{4 3}{4 5}

Multiply by the Conjugate

\frac{4 3 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 3 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 375}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 375}{5}

z = \pm \frac{4 375}{5}

Separate the equation into 2 possible cases

z = \frac{4 375}{5} z = - \frac{4 375}{5}

z = 0 z = \frac{4 375}{5} z = - \frac{4 375}{5}

Solution

z_{1} = - \frac{4 375}{5}, z_{2} = 0, z_{3} = \frac{4 375}{5}

Alternative Form

z_{1} \approx - 0.880112, z_{2} = 0, z_{3} \approx 0.880112

Show Solution