x^2-14x+12=-2x+1

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Solution for x^2-14x+12=-2x+1 equation: 


Simplifying
x2 + -14x + 12 = -2x + 1

Reorder the terms:
12 + -14x + x2 = -2x + 1

Reorder the terms:
12 + -14x + x2 = 1 + -2x

Solving
12 + -14x + x2 = 1 + -2x

Solving for variable 'x'.

Reorder the terms:
12 + -1 + -14x + 2x + x2 = 1 + -2x + -1 + 2x

Combine like terms: 12 + -1 = 11
11 + -14x + 2x + x2 = 1 + -2x + -1 + 2x

Combine like terms: -14x + 2x = -12x
11 + -12x + x2 = 1 + -2x + -1 + 2x

Reorder the terms:
11 + -12x + x2 = 1 + -1 + -2x + 2x

Combine like terms: 1 + -1 = 0
11 + -12x + x2 = 0 + -2x + 2x
11 + -12x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
11 + -12x + x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 11}

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