x^2=39x-108

Solution for x^2=39x-108 equation:

Simplifying
x2 = 39x + -108

Reorder the terms:
x2 = -108 + 39x

Solving
x2 = -108 + 39x

Solving for variable 'x'.

Reorder the terms:
108 + -39x + x2 = -108 + 39x + 108 + -39x

Reorder the terms:
108 + -39x + x2 = -108 + 108 + 39x + -39x

Combine like terms: -108 + 108 = 0
108 + -39x + x2 = 0 + 39x + -39x
108 + -39x + x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
108 + -39x + x2 = 0

Factor a trinomial.
(3 + -1x)(36 + -1x) = 0

Subproblem 1
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 2
Set the factor '(36 + -1x)' equal to zero and attempt to solve:

Simplifying
36 + -1x = 0

Solving
36 + -1x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1x = 0 + -36
-1x = 0 + -36

Combine like terms: 0 + -36 = -36
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36
Solution
x = {3, 36}