x^2-12x+36=x+14

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Solution for x^2-12x+36=x+14 equation: 


Simplifying
x2 + -12x + 36 = x + 14

Reorder the terms:
36 + -12x + x2 = x + 14

Reorder the terms:
36 + -12x + x2 = 14 + x

Solving
36 + -12x + x2 = 14 + x

Solving for variable 'x'.

Reorder the terms:
36 + -14 + -12x + -1x + x2 = 14 + x + -14 + -1x

Combine like terms: 36 + -14 = 22
22 + -12x + -1x + x2 = 14 + x + -14 + -1x

Combine like terms: -12x + -1x = -13x
22 + -13x + x2 = 14 + x + -14 + -1x

Reorder the terms:
22 + -13x + x2 = 14 + -14 + x + -1x

Combine like terms: 14 + -14 = 0
22 + -13x + x2 = 0 + x + -1x
22 + -13x + x2 = x + -1x

Combine like terms: x + -1x = 0
22 + -13x + x2 = 0

Factor a trinomial.
(2 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {2, 11}

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