(-x^2+6x)-(-2x+12)=(6-x)(x-2)

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Solution for (-x^2+6x)-(-2x+12)=(6-x)(x-2) equation: 


Simplifying
(-1x2 + 6x) + -1(-2x + 12) = (6 + -1x)(x + -2)

Reorder the terms:
(6x + -1x2) + -1(-2x + 12) = (6 + -1x)(x + -2)

Remove parenthesis around (6x + -1x2)
6x + -1x2 + -1(-2x + 12) = (6 + -1x)(x + -2)

Reorder the terms:
6x + -1x2 + -1(12 + -2x) = (6 + -1x)(x + -2)
6x + -1x2 + (12 * -1 + -2x * -1) = (6 + -1x)(x + -2)
6x + -1x2 + (-12 + 2x) = (6 + -1x)(x + -2)

Reorder the terms:
-12 + 6x + 2x + -1x2 = (6 + -1x)(x + -2)

Combine like terms: 6x + 2x = 8x
-12 + 8x + -1x2 = (6 + -1x)(x + -2)

Reorder the terms:
-12 + 8x + -1x2 = (6 + -1x)(-2 + x)

Multiply (6 + -1x) * (-2 + x)
-12 + 8x + -1x2 = (6(-2 + x) + -1x * (-2 + x))
-12 + 8x + -1x2 = ((-2 * 6 + x * 6) + -1x * (-2 + x))
-12 + 8x + -1x2 = ((-12 + 6x) + -1x * (-2 + x))
-12 + 8x + -1x2 = (-12 + 6x + (-2 * -1x + x * -1x))
-12 + 8x + -1x2 = (-12 + 6x + (2x + -1x2))

Combine like terms: 6x + 2x = 8x
-12 + 8x + -1x2 = (-12 + 8x + -1x2)

Add '12' to each side of the equation.
-12 + 8x + 12 + -1x2 = -12 + 8x + 12 + -1x2

Reorder the terms:
-12 + 12 + 8x + -1x2 = -12 + 8x + 12 + -1x2

Combine like terms: -12 + 12 = 0
0 + 8x + -1x2 = -12 + 8x + 12 + -1x2
8x + -1x2 = -12 + 8x + 12 + -1x2

Reorder the terms:
8x + -1x2 = -12 + 12 + 8x + -1x2

Combine like terms: -12 + 12 = 0
8x + -1x2 = 0 + 8x + -1x2
8x + -1x2 = 8x + -1x2

Add '-8x' to each side of the equation.
8x + -8x + -1x2 = 8x + -8x + -1x2

Combine like terms: 8x + -8x = 0
0 + -1x2 = 8x + -8x + -1x2
-1x2 = 8x + -8x + -1x2

Combine like terms: 8x + -8x = 0
-1x2 = 0 + -1x2
-1x2 = -1x2

Add 'x2' to each side of the equation.
-1x2 + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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