(x-2)*(x-3)-(x-6)*(x+1)=12

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Solution for (x-2)*(x-3)-(x-6)*(x+1)=12 equation: 


Simplifying
(x + -2)(x + -3) + -1(x + -6)(x + 1) = 12

Reorder the terms:
(-2 + x)(x + -3) + -1(x + -6)(x + 1) = 12

Reorder the terms:
(-2 + x)(-3 + x) + -1(x + -6)(x + 1) = 12

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) + -1(x + -6)(x + 1) = 12
((-3 * -2 + x * -2) + x(-3 + x)) + -1(x + -6)(x + 1) = 12
((6 + -2x) + x(-3 + x)) + -1(x + -6)(x + 1) = 12
(6 + -2x + (-3 * x + x * x)) + -1(x + -6)(x + 1) = 12
(6 + -2x + (-3x + x2)) + -1(x + -6)(x + 1) = 12

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) + -1(x + -6)(x + 1) = 12

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

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

Multiply (-6 + x) * (1 + x)
6 + -5x + x2 + -1(-6(1 + x) + x(1 + x)) = 12
6 + -5x + x2 + -1((1 * -6 + x * -6) + x(1 + x)) = 12
6 + -5x + x2 + -1((-6 + -6x) + x(1 + x)) = 12
6 + -5x + x2 + -1(-6 + -6x + (1 * x + x * x)) = 12
6 + -5x + x2 + -1(-6 + -6x + (1x + x2)) = 12

Combine like terms: -6x + 1x = -5x
6 + -5x + x2 + -1(-6 + -5x + x2) = 12
6 + -5x + x2 + (-6 * -1 + -5x * -1 + x2 * -1) = 12
6 + -5x + x2 + (6 + 5x + -1x2) = 12

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

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

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

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

Add '-12' to each side of the equation.
12 + -12 = 12 + -12

Combine like terms: 12 + -12 = 0
0 = 12 + -12

Combine like terms: 12 + -12 = 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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