Solve 12s^3-3-2s 18s^2

Question

Simplify the expression

Solution

- 24 s^{3} - 3

Evaluate

12 s^{3} - 3 - 2 s \times 18 s^{2}

Multiply

More Steps

Multiply the terms

- 2 s \times 18 s^{2}

Multiply the terms

- 36 s \times s^{2}

Multiply the terms with the same base by adding their exponents

- 36 s^{1 + 2}

Add the numbers

- 36 s^{3}

12 s^{3} - 3 - 36 s^{3}

Solution

More Steps

Evaluate

12 s^{3} - 36 s^{3}

Collect like terms by calculating the sum or difference of their coefficients

(12 - 36) s^{3}

Subtract the numbers

- 24 s^{3}

- 24 s^{3} - 3

Show Solution

Factor the expression

Factor

- 3 (2 s + 1) (4 s^{2} - 2 s + 1)

Evaluate

12 s^{3} - 3 - 2 s \times 18 s^{2}

Multiply

More Steps

Multiply the terms

2 s \times 18 s^{2}

Multiply the terms

36 s \times s^{2}

Multiply the terms with the same base by adding their exponents

36 s^{1 + 2}

Add the numbers

36 s^{3}

12 s^{3} - 3 - 36 s^{3}

Subtract the terms

More Steps

Evaluate

12 s^{3} - 36 s^{3}

Collect like terms by calculating the sum or difference of their coefficients

(12 - 36) s^{3}

Subtract the numbers

- 24 s^{3}

- 24 s^{3} - 3

Rewrite the expression

- 3 \times 8 s^{3} - 3

Factor out - 3 from the expression

- 3 (8 s^{3} + 1)

Solution

More Steps

Evaluate

8 s^{3} + 1

Calculate

8 s^{3} - 4 s^{2} + 2 s + 4 s^{2} - 2 s + 1

Rewrite the expression

2 s \times 4 s^{2} - 2 s \times 2 s + 2 s + 4 s^{2} - 2 s + 1

Factor out 2 s from the expression

2 s (4 s^{2} - 2 s + 1) + 4 s^{2} - 2 s + 1

Factor out 4 s^{2} - 2 s + 1 from the expression

(2 s + 1) (4 s^{2} - 2 s + 1)

- 3 (2 s + 1) (4 s^{2} - 2 s + 1)

Show Solution

Find the roots

Find the roots of the algebra expression

s = - \frac{1}{2}

Alternative Form

s = - 0.5

Evaluate

12 s^{3} - 3 - 2 s \times 18 s^{2}

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

12 s^{3} - 3 - 2 s \times 18 s^{2} = 0

Multiply

More Steps

Multiply the terms

2 s \times 18 s^{2}

Multiply the terms

36 s \times s^{2}

Multiply the terms with the same base by adding their exponents

36 s^{1 + 2}

Add the numbers

36 s^{3}

12 s^{3} - 3 - 36 s^{3} = 0

Subtract the terms

More Steps

Simplify

12 s^{3} - 3 - 36 s^{3}

Subtract the terms

More Steps

Evaluate

12 s^{3} - 36 s^{3}

Collect like terms by calculating the sum or difference of their coefficients

(12 - 36) s^{3}

Subtract the numbers

- 24 s^{3}

- 24 s^{3} - 3

- 24 s^{3} - 3 = 0

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

- 24 s^{3} = 0 + 3

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

- 24 s^{3} = 3

Change the signs on both sides of the equation

24 s^{3} = - 3

Divide both sides

\frac{24 s ^{3}}{24} = \frac{- 3}{24}

Divide the numbers

s^{3} = \frac{- 3}{24}

Divide the numbers

More Steps

Evaluate

\frac{- 3}{24}

Cancel out the common factor 3

\frac{- 1}{8}

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

- \frac{1}{8}

s^{3} = - \frac{1}{8}

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

3 s^{3} = 3 - \frac{1}{8}

Calculate

s = 3 - \frac{1}{8}

Solution

More Steps

Evaluate

3 - \frac{1}{8}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{8}

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

- \frac{3 1}{3 8}

Simplify the radical expression

- \frac{1}{3 8}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

- \frac{1}{2}

s = - \frac{1}{2}

Alternative Form

s = - 0.5

Show Solution

12s^3 3 2s 18s^2

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression