x^2-12x+37=x-3

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Solution for x^2-12x+37=x-3 equation: 


Simplifying
x2 + -12x + 37 = x + -3

Reorder the terms:
37 + -12x + x2 = x + -3

Reorder the terms:
37 + -12x + x2 = -3 + x

Solving
37 + -12x + x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
37 + 3 + -12x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: 37 + 3 = 40
40 + -12x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: -12x + -1x = -13x
40 + -13x + x2 = -3 + x + 3 + -1x

Reorder the terms:
40 + -13x + x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
40 + -13x + x2 = 0 + x + -1x
40 + -13x + x2 = x + -1x

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

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

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

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