x^2-6x=5x-12-x^2

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Solution for x^2-6x=5x-12-x^2 equation: 


Simplifying
x2 + -6x = 5x + -12 + -1x2

Reorder the terms:
-6x + x2 = 5x + -12 + -1x2

Reorder the terms:
-6x + x2 = -12 + 5x + -1x2

Solving
-6x + x2 = -12 + 5x + -1x2

Solving for variable 'x'.

Reorder the terms:
12 + -6x + -5x + x2 + x2 = -12 + 5x + -1x2 + 12 + -5x + x2

Combine like terms: -6x + -5x = -11x
12 + -11x + x2 + x2 = -12 + 5x + -1x2 + 12 + -5x + x2

Combine like terms: x2 + x2 = 2x2
12 + -11x + 2x2 = -12 + 5x + -1x2 + 12 + -5x + x2

Reorder the terms:
12 + -11x + 2x2 = -12 + 12 + 5x + -5x + -1x2 + x2

Combine like terms: -12 + 12 = 0
12 + -11x + 2x2 = 0 + 5x + -5x + -1x2 + x2
12 + -11x + 2x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
12 + -11x + 2x2 = 0 + -1x2 + x2
12 + -11x + 2x2 = -1x2 + x2

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

Factor a trinomial.
(3 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1.5, 4}

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