Solve 12b^3-56b^2-96b

Question

Factor the expression

4 b (b - 6) (3 b + 4)

Evaluate

12 b^{3} - 56 b^{2} - 96 b

Rewrite the expression

4 b \times 3 b^{2} - 4 b \times 14 b - 4 b \times 24

Factor out 4 b from the expression

4 b (3 b^{2} - 14 b - 24)

Solution

More Steps

Evaluate

3 b^{2} - 14 b - 24

Rewrite the expression

3 b^{2} + (4 - 18) b - 24

Calculate

3 b^{2} + 4 b - 18 b - 24

Rewrite the expression

b \times 3 b + b \times 4 - 6 \times 3 b - 6 \times 4

Factor out b from the expression

b (3 b + 4) - 6 \times 3 b - 6 \times 4

Factor out - 6 from the expression

b (3 b + 4) - 6 (3 b + 4)

Factor out 3 b + 4 from the expression

(b - 6) (3 b + 4)

4 b (b - 6) (3 b + 4)

Show Solution

b_{1} = - \frac{4}{3}, b_{2} = 0, b_{3} = 6

Alternative Form

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

Evaluate

12 b^{3} - 56 b^{2} - 96 b

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

12 b^{3} - 56 b^{2} - 96 b = 0

Factor the expression

4 b (b - 6) (3 b + 4) = 0

Divide both sides

b (b - 6) (3 b + 4) = 0

Separate the equation into 3 possible cases

b = 0 b - 6 = 0 3 b + 4 = 0

Solve the equation

More Steps

Evaluate

b - 6 = 0

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

b = 0 + 6

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

b = 6

b = 0 b = 6 3 b + 4 = 0

Solve the equation

More Steps

Evaluate

3 b + 4 = 0

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

3 b = 0 - 4

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

3 b = - 4

Divide both sides

\frac{3 b}{3} = \frac{- 4}{3}

Divide the numbers

b = \frac{- 4}{3}

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

b = - \frac{4}{3}

b = 0 b = 6 b = - \frac{4}{3}

Solution

b_{1} = - \frac{4}{3}, b_{2} = 0, b_{3} = 6

Alternative Form

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

Show Solution