Solve 12x^(3)-9x^(2) 4x-3

Question

Simplify the expression

- 24 x^{3} - 3

Evaluate

12 x^{3} - 9 x^{2} \times 4 x - 3

Multiply

More Steps

Multiply the terms

- 9 x^{2} \times 4 x

Multiply the terms

- 36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 36 x^{2 + 1}

Add the numbers

- 36 x^{3}

12 x^{3} - 36 x^{3} - 3

Solution

More Steps

Evaluate

12 x^{3} - 36 x^{3}

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

(12 - 36) x^{3}

Subtract the numbers

- 24 x^{3}

- 24 x^{3} - 3

Show Solution

Factor the expression

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

Evaluate

12 x^{3} - 9 x^{2} \times 4 x - 3

Multiply

More Steps

Multiply the terms

9 x^{2} \times 4 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

12 x^{3} - 36 x^{3} - 3

Subtract the terms

More Steps

Simplify

12 x^{3} - 36 x^{3}

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

(12 - 36) x^{3}

Subtract the numbers

- 24 x^{3}

- 24 x^{3} - 3

Rewrite the expression

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

Factor out - 3 from the expression

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

Solution

More Steps

Evaluate

8 x^{3} + 1

Calculate

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

Rewrite the expression

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

Factor out 2 x from the expression

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

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

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

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

Show Solution

Find the roots

x = - \frac{1}{2}

Alternative Form

x = - 0.5

Evaluate

12 x^{3} - 9 x^{2} \times 4 x - 3

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

12 x^{3} - 9 x^{2} \times 4 x - 3 = 0

Multiply

More Steps

Multiply the terms

9 x^{2} \times 4 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

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

Subtract the terms

More Steps

Simplify

12 x^{3} - 36 x^{3}

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

(12 - 36) x^{3}

Subtract the numbers

- 24 x^{3}

- 24 x^{3} - 3 = 0

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

- 24 x^{3} = 0 + 3

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

- 24 x^{3} = 3

Change the signs on both sides of the equation

24 x^{3} = - 3

Divide both sides

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

Divide the numbers

x^{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}

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

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

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

Calculate

x = 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}

x = - \frac{1}{2}

Alternative Form

x = - 0.5

Show Solution