x^2-12x=5x-66

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Solution for x^2-12x=5x-66 equation: 


Simplifying
x2 + -12x = 5x + -66

Reorder the terms:
-12x + x2 = 5x + -66

Reorder the terms:
-12x + x2 = -66 + 5x

Solving
-12x + x2 = -66 + 5x

Solving for variable 'x'.

Reorder the terms:
66 + -12x + -5x + x2 = -66 + 5x + 66 + -5x

Combine like terms: -12x + -5x = -17x
66 + -17x + x2 = -66 + 5x + 66 + -5x

Reorder the terms:
66 + -17x + x2 = -66 + 66 + 5x + -5x

Combine like terms: -66 + 66 = 0
66 + -17x + x2 = 0 + 5x + -5x
66 + -17x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
66 + -17x + x2 = 0

Factor a trinomial.
(6 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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 = {6, 11}

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