Solve - 3(2z^22z-2)

Question

Simplify the expression

- 12 z^{3} + 6

Evaluate

- 3 (2 z^{2} \times 2 z - 2)

Multiply

More Steps

Evaluate

2 z^{2} \times 2 z

Multiply the terms

4 z^{2} \times z

Multiply the terms with the same base by adding their exponents

4 z^{2 + 1}

Add the numbers

4 z^{3}

- 3 (4 z^{3} - 2)

Apply the distributive property

- 3 \times 4 z^{3} - (- 3 \times 2)

Multiply the numbers

- 12 z^{3} - (- 3 \times 2)

Multiply the numbers

- 12 z^{3} - (- 6)

Solution

- 12 z^{3} + 6

Show Solution

Factor the expression

- 6 (2 z^{3} - 1)

Evaluate

- 3 (2 z^{2} \times 2 z - 2)

Multiply

More Steps

Evaluate

2 z^{2} \times 2 z

Multiply the terms

4 z^{2} \times z

Multiply the terms with the same base by adding their exponents

4 z^{2 + 1}

Add the numbers

4 z^{3}

- 3 (4 z^{3} - 2)

Factor the expression

- 3 \times 2 (2 z^{3} - 1)

Solution

- 6 (2 z^{3} - 1)

Show Solution

Find the roots

z = \frac{3 4}{2}

Alternative Form

z \approx 0.793701

Evaluate

- 3 (2 z^{2} \times 2 z - 2)

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

- 3 (2 z^{2} \times 2 z - 2) = 0

Multiply

More Steps

Multiply the terms

2 z^{2} \times 2 z

Multiply the terms

4 z^{2} \times z

Multiply the terms with the same base by adding their exponents

4 z^{2 + 1}

Add the numbers

4 z^{3}

- 3 (4 z^{3} - 2) = 0

Change the sign

3 (4 z^{3} - 2) = 0

Rewrite the expression

4 z^{3} - 2 = 0

Move the constant to the right side

4 z^{3} = 2

Divide both sides

\frac{4 z ^{3}}{4} = \frac{2}{4}

Divide the numbers

z^{3} = \frac{2}{4}

Cancel out the common factor 2

z^{3} = \frac{1}{2}

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

3 z^{3} = 3 \frac{1}{2}

Calculate

z = 3 \frac{1}{2}

Solution

More Steps

Evaluate

3 \frac{1}{2}

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

\frac{3 1}{3 2}

Simplify the radical expression

\frac{1}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

The product of roots with the same index is equal to the root of the product

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 4}{2}

z = \frac{3 4}{2}

Alternative Form

z \approx 0.793701

Show Solution