108=x(23+x)

Solution for 108=x(23+x) equation:

Simplifying
108 = x(23 + x)
108 = (23 * x + x * x)
108 = (23x + x2)

Solving
108 = 23x + x2

Solving for variable 'x'.

Reorder the terms:
108 + -23x + -1x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
108 + -23x + -1x2 = 0 + x2 + -1x2
108 + -23x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
108 + -23x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(27 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(27 + x)' equal to zero and attempt to solve:

Simplifying
27 + x = 0

Solving
27 + x = 0

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

Add '-27' to each side of the equation.
27 + -27 + x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + x = 0 + -27
x = 0 + -27

Combine like terms: 0 + -27 = -27
x = -27

Simplifying
x = -27
Solution
x = {4, -27}