x-4=x^2-12x+36

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Solution for x-4=x^2-12x+36 equation: 


Simplifying
x + -4 = x2 + -12x + 36

Reorder the terms:
-4 + x = x2 + -12x + 36

Reorder the terms:
-4 + x = 36 + -12x + x2

Solving
-4 + x = 36 + -12x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -36 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Combine like terms: -4 + -36 = -40
-40 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Combine like terms: x + 12x = 13x
-40 + 13x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Reorder the terms:
-40 + 13x + -1x2 = 36 + -36 + -12x + 12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-40 + 13x + -1x2 = 0 + -12x + 12x + x2 + -1x2
-40 + 13x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-40 + 13x + -1x2 = 0 + x2 + -1x2
-40 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + 13x + -1x2 = 0

Factor a trinomial.
(-8 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {8, 5}

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