Solve 6x^3-12x^2-48x

Question

Factor the expression

6 x (x - 4) (x + 2)

Evaluate

6 x^{3} - 12 x^{2} - 48 x

Rewrite the expression

6 x \times x^{2} - 6 x \times 2 x - 6 x \times 8

Factor out 6 x from the expression

6 x (x^{2} - 2 x - 8)

Solution

More Steps

Evaluate

x^{2} - 2 x - 8

Rewrite the expression

x^{2} + (2 - 4) x - 8

Calculate

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

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 4 from the expression

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

Factor out x + 2 from the expression

(x - 4) (x + 2)

6 x (x - 4) (x + 2)

Show Solution

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

Evaluate

6 x^{3} - 12 x^{2} - 48 x

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

6 x^{3} - 12 x^{2} - 48 x = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 3 possible cases

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

Solve the equation

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = 0 x = 4 x = - 2

Solution

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

Show Solution