Solve 9x^3-30x^2-24x

Question

Factor the expression

3 x (x - 4) (3 x + 2)

Evaluate

9 x^{3} - 30 x^{2} - 24 x

Rewrite the expression

3 x \times 3 x^{2} - 3 x \times 10 x - 3 x \times 8

Factor out 3 x from the expression

3 x (3 x^{2} - 10 x - 8)

Solution

More Steps

Evaluate

3 x^{2} - 10 x - 8

Rewrite the expression

3 x^{2} + (2 - 12) x - 8

Calculate

3 x^{2} + 2 x - 12 x - 8

Rewrite the expression

x \times 3 x + x \times 2 - 4 \times 3 x - 4 \times 2

Factor out x from the expression

x (3 x + 2) - 4 \times 3 x - 4 \times 2

Factor out - 4 from the expression

x (3 x + 2) - 4 (3 x + 2)

Factor out 3 x + 2 from the expression

(x - 4) (3 x + 2)

3 x (x - 4) (3 x + 2)

Show Solution

x_{1} = - \frac{2}{3}, x_{2} = 0, x_{3} = 4

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0, x_{3} = 4

Evaluate

9 x^{3} - 30 x^{2} - 24 x

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

9 x^{3} - 30 x^{2} - 24 x = 0

Factor the expression

3 x (x - 4) (3 x + 2) = 0

Divide both sides

x (x - 4) (3 x + 2) = 0

Separate the equation into 3 possible cases

x = 0 x - 4 = 0 3 x + 2 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 0 x = 4 3 x + 2 = 0

Solve the equation

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

\frac{3 x}{3} = \frac{- 2}{3}

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

x = 0 x = 4 x = - \frac{2}{3}

Solution

x_{1} = - \frac{2}{3}, x_{2} = 0, x_{3} = 4

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0, x_{3} = 4

Show Solution