x^2=21x-108

Solution for x^2=21x-108 equation:

Simplifying
x2 = 21x + -108

Reorder the terms:
x2 = -108 + 21x

Solving
x2 = -108 + 21x

Solving for variable 'x'.

Reorder the terms:
108 + -21x + x2 = -108 + 21x + 108 + -21x

Reorder the terms:
108 + -21x + x2 = -108 + 108 + 21x + -21x

Combine like terms: -108 + 108 = 0
108 + -21x + x2 = 0 + 21x + -21x
108 + -21x + x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
108 + -21x + x2 = 0

Factor a trinomial.
(9 + -1x)(12 + -1x) = 0

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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {9, 12}