x^2+x(x+6)=108

Solution for x^2+x(x+6)=108 equation:

Simplifying
x2 + x(x + 6) = 108

Reorder the terms:
x2 + x(6 + x) = 108
x2 + (6 * x + x * x) = 108
x2 + (6x + x2) = 108

Reorder the terms:
6x + x2 + x2 = 108

Combine like terms: x2 + x2 = 2x2
6x + 2x2 = 108

Solving
6x + 2x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + 6x + 2x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 3x + x2) = 0

Factor a trinomial.
2((-9 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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 = {-9, 6}