x(x-6)(x+1)=0

Solution for x(x-6)(x+1)=0 equation:

Simplifying
x(x + -6)(x + 1) = 0

Reorder the terms:
x(-6 + x)(x + 1) = 0

Reorder the terms:
x(-6 + x)(1 + x) = 0

Multiply (-6 + x) * (1 + x)
x(-6(1 + x) + x(1 + x)) = 0
x((1 * -6 + x * -6) + x(1 + x)) = 0
x((-6 + -6x) + x(1 + x)) = 0
x(-6 + -6x + (1 * x + x * x)) = 0
x(-6 + -6x + (1x + x2)) = 0

Combine like terms: -6x + 1x = -5x
x(-6 + -5x + x2) = 0
(-6 * x + -5x * x + x2 * x) = 0
(-6x + -5x2 + x3) = 0

Solving
-6x + -5x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -5x + x2) = 0

Factor a trinomial.
x((-1 + -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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
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, -1, 6}