Solve 10z^23z - 6

Question

Simplify the expression

30 z^{3} - 6

Evaluate

10 z^{2} \times 3 z - 6

Solution

More Steps

Evaluate

10 z^{2} \times 3 z

Multiply the terms

30 z^{2} \times z

Multiply the terms with the same base by adding their exponents

30 z^{2 + 1}

Add the numbers

30 z^{3}

30 z^{3} - 6

Show Solution

Factor the expression

6 (5 z^{3} - 1)

Evaluate

10 z^{2} \times 3 z - 6

Multiply

More Steps

Evaluate

10 z^{2} \times 3 z

Multiply the terms

30 z^{2} \times z

Multiply the terms with the same base by adding their exponents

30 z^{2 + 1}

Add the numbers

30 z^{3}

30 z^{3} - 6

Solution

6 (5 z^{3} - 1)

Show Solution

Find the roots

z = \frac{3 25}{5}

Alternative Form

z \approx 0.584804

Evaluate

10 z^{2} \times 3 z - 6

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

10 z^{2} \times 3 z - 6 = 0

Multiply

More Steps

Multiply the terms

10 z^{2} \times 3 z

Multiply the terms

30 z^{2} \times z

Multiply the terms with the same base by adding their exponents

30 z^{2 + 1}

Add the numbers

30 z^{3}

30 z^{3} - 6 = 0

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

30 z^{3} = 0 + 6

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

30 z^{3} = 6

Divide both sides

\frac{30 z ^{3}}{30} = \frac{6}{30}

Divide the numbers

z^{3} = \frac{6}{30}

Cancel out the common factor 6

z^{3} = \frac{1}{5}

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

3 z^{3} = 3 \frac{1}{5}

Calculate

z = 3 \frac{1}{5}

Solution

More Steps

Evaluate

3 \frac{1}{5}

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

\frac{3 1}{3 5}

Simplify the radical expression

\frac{1}{3 5}

Multiply by the Conjugate

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

Simplify

\frac{3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 25}{5}

z = \frac{3 25}{5}

Alternative Form

z \approx 0.584804

Show Solution