x(x+3)(x-6)=0

Solution for x(x+3)(x-6)=0 equation:

Simplifying
x(x + 3)(x + -6) = 0

Reorder the terms:
x(3 + x)(x + -6) = 0

Reorder the terms:
x(3 + x)(-6 + x) = 0

Multiply (3 + x) * (-6 + x)
x(3(-6 + x) + x(-6 + x)) = 0
x((-6 * 3 + x * 3) + x(-6 + x)) = 0
x((-18 + 3x) + x(-6 + x)) = 0
x(-18 + 3x + (-6 * x + x * x)) = 0
x(-18 + 3x + (-6x + x2)) = 0

Combine like terms: 3x + -6x = -3x
x(-18 + -3x + x2) = 0
(-18 * x + -3x * x + x2 * x) = 0
(-18x + -3x2 + x3) = 0

Solving
-18x + -3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + -3x + x2) = 0

Factor a trinomial.
x((-3 + -1x)(6 + -1x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -3, 6}