Solve x^3-3x^2-6x 18

Question

Simplify the expression

x^{3} - 3 x^{2} - 108 x

Evaluate

x^{3} - 3 x^{2} - 6 x \times 18

Solution

x^{3} - 3 x^{2} - 108 x

Show Solution

x (x - 12) (x + 9)

Evaluate

x^{3} - 3 x^{2} - 6 x \times 18

Multiply the terms

x^{3} - 3 x^{2} - 108 x

Rewrite the expression

x \times x^{2} - x \times 3 x - x \times 108

Factor out x from the expression

x (x^{2} - 3 x - 108)

Solution

More Steps

Evaluate

x^{2} - 3 x - 108

Rewrite the expression

x^{2} + (9 - 12) x - 108

Calculate

x^{2} + 9 x - 12 x - 108

Rewrite the expression

x \times x + x \times 9 - 12 x - 12 \times 9

Factor out x from the expression

x (x + 9) - 12 x - 12 \times 9

Factor out - 12 from the expression

x (x + 9) - 12 (x + 9)

Factor out x + 9 from the expression

(x - 12) (x + 9)

x (x - 12) (x + 9)

Show Solution

x_{1} = - 9, x_{2} = 0, x_{3} = 12

Evaluate

x^{3} - 3 x^{2} - 6 x \times 18

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

x^{3} - 3 x^{2} - 6 x \times 18 = 0

Multiply the terms

x^{3} - 3 x^{2} - 108 x = 0

Factor the expression

x (x - 12) (x + 9) = 0

Separate the equation into 3 possible cases

x = 0 x - 12 = 0 x + 9 = 0

Solve the equation

More Steps

Evaluate

x - 12 = 0

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

x = 0 + 12

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

x = 12

x = 0 x = 12 x + 9 = 0

Solve the equation

More Steps

Evaluate

x + 9 = 0

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

x = 0 - 9

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

x = - 9

x = 0 x = 12 x = - 9

Solution

x_{1} = - 9, x_{2} = 0, x_{3} = 12

Show Solution