(x-2)(x+3)-x(2x+1)-2(x+2)=-x(x+12)+10(x-1)

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Solution for (x-2)(x+3)-x(2x+1)-2(x+2)=-x(x+12)+10(x-1) equation: 


Simplifying
(x + -2)(x + 3) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Reorder the terms:
(-2 + x)(x + 3) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Reorder the terms:
(-2 + x)(3 + x) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
((3 * -2 + x * -2) + x(3 + x)) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
((-6 + -2x) + x(3 + x)) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
(-6 + -2x + (3 * x + x * x)) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
(-6 + -2x + (3x + x2)) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) + -1x(2x + 1) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Reorder the terms:
-6 + 1x + x2 + -1x(1 + 2x) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
-6 + 1x + x2 + (1 * -1x + 2x * -1x) + -2(x + 2) = -1x(x + 12) + 10(x + -1)
-6 + 1x + x2 + (-1x + -2x2) + -2(x + 2) = -1x(x + 12) + 10(x + -1)

Reorder the terms:
-6 + 1x + x2 + -1x + -2x2 + -2(2 + x) = -1x(x + 12) + 10(x + -1)
-6 + 1x + x2 + -1x + -2x2 + (2 * -2 + x * -2) = -1x(x + 12) + 10(x + -1)
-6 + 1x + x2 + -1x + -2x2 + (-4 + -2x) = -1x(x + 12) + 10(x + -1)

Reorder the terms:
-6 + -4 + 1x + -1x + -2x + x2 + -2x2 = -1x(x + 12) + 10(x + -1)

Combine like terms: -6 + -4 = -10
-10 + 1x + -1x + -2x + x2 + -2x2 = -1x(x + 12) + 10(x + -1)

Combine like terms: 1x + -1x = 0
-10 + 0 + -2x + x2 + -2x2 = -1x(x + 12) + 10(x + -1)
-10 + -2x + x2 + -2x2 = -1x(x + 12) + 10(x + -1)

Combine like terms: x2 + -2x2 = -1x2
-10 + -2x + -1x2 = -1x(x + 12) + 10(x + -1)

Reorder the terms:
-10 + -2x + -1x2 = -1x(12 + x) + 10(x + -1)
-10 + -2x + -1x2 = (12 * -1x + x * -1x) + 10(x + -1)
-10 + -2x + -1x2 = (-12x + -1x2) + 10(x + -1)

Reorder the terms:
-10 + -2x + -1x2 = -12x + -1x2 + 10(-1 + x)
-10 + -2x + -1x2 = -12x + -1x2 + (-1 * 10 + x * 10)
-10 + -2x + -1x2 = -12x + -1x2 + (-10 + 10x)

Reorder the terms:
-10 + -2x + -1x2 = -10 + -12x + 10x + -1x2

Combine like terms: -12x + 10x = -2x
-10 + -2x + -1x2 = -10 + -2x + -1x2

Add '10' to each side of the equation.
-10 + -2x + 10 + -1x2 = -10 + -2x + 10 + -1x2

Reorder the terms:
-10 + 10 + -2x + -1x2 = -10 + -2x + 10 + -1x2

Combine like terms: -10 + 10 = 0
0 + -2x + -1x2 = -10 + -2x + 10 + -1x2
-2x + -1x2 = -10 + -2x + 10 + -1x2

Reorder the terms:
-2x + -1x2 = -10 + 10 + -2x + -1x2

Combine like terms: -10 + 10 = 0
-2x + -1x2 = 0 + -2x + -1x2
-2x + -1x2 = -2x + -1x2

Add '2x' to each side of the equation.
-2x + 2x + -1x2 = -2x + 2x + -1x2

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

Combine like terms: -2x + 2x = 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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