Solve 2x^3-2x^2-12x

Question

Factor the expression

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

Evaluate

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

Rewrite the expression

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

Factor out 2 x from the expression

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

Solution

More Steps

Evaluate

x^{2} - x - 6

Rewrite the expression

x^{2} + (2 - 3) x - 6

Calculate

x^{2} + 2 x - 3 x - 6

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 3 from the expression

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

Factor out x + 2 from the expression

(x - 3) (x + 2)

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

Show Solution

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

Evaluate

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

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

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

Factor the expression

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

Divide both sides

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

Separate the equation into 3 possible cases

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

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3 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 = 3 x = - 2

Solution

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

Show Solution