[x^2+x][x-6]=0

Solution for [x^2+x][x-6]=0 equation:

Simplifying
[x2 + x][x + -6] = 0

Reorder the terms:
[x + x2][x + -6] = 0

Reorder the terms:
[x + x2][-6 + x] = 0

Multiply [x + x2] * [-6 + x]
[x[-6 + x] + x2[-6 + x]] = 0
[[-6 * x + x * x] + x2[-6 + x]] = 0
[[-6x + x2] + x2[-6 + x]] = 0
[-6x + x2 + [-6 * x2 + x * x2]] = 0
[-6x + x2 + [-6x2 + x3]] = 0

Combine like terms: x2 + -6x2 = -5x2
[-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}