x^2=12x-20

Solution for x^2=12x-20 equation:

Simplifying
x2 = 12x + -20

Reorder the terms:
x2 = -20 + 12x

Solving
x2 = -20 + 12x

Solving for variable 'x'.

Reorder the terms:
20 + -12x + x2 = -20 + 12x + 20 + -12x

Reorder the terms:
20 + -12x + x2 = -20 + 20 + 12x + -12x

Combine like terms: -20 + 20 = 0
20 + -12x + x2 = 0 + 12x + -12x
20 + -12x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
20 + -12x + x2 = 0

Factor a trinomial.
(2 + -1x)(10 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}