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

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


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

Reorder the terms:
12(-3 + x) + -1(x + 2) = (x + 2)(x + -3)
(-3 * 12 + x * 12) + -1(x + 2) = (x + 2)(x + -3)
(-36 + 12x) + -1(x + 2) = (x + 2)(x + -3)

Reorder the terms:
-36 + 12x + -1(2 + x) = (x + 2)(x + -3)
-36 + 12x + (2 * -1 + x * -1) = (x + 2)(x + -3)
-36 + 12x + (-2 + -1x) = (x + 2)(x + -3)

Reorder the terms:
-36 + -2 + 12x + -1x = (x + 2)(x + -3)

Combine like terms: -36 + -2 = -38
-38 + 12x + -1x = (x + 2)(x + -3)

Combine like terms: 12x + -1x = 11x
-38 + 11x = (x + 2)(x + -3)

Reorder the terms:
-38 + 11x = (2 + x)(x + -3)

Reorder the terms:
-38 + 11x = (2 + x)(-3 + x)

Multiply (2 + x) * (-3 + x)
-38 + 11x = (2(-3 + x) + x(-3 + x))
-38 + 11x = ((-3 * 2 + x * 2) + x(-3 + x))
-38 + 11x = ((-6 + 2x) + x(-3 + x))
-38 + 11x = (-6 + 2x + (-3 * x + x * x))
-38 + 11x = (-6 + 2x + (-3x + x2))

Combine like terms: 2x + -3x = -1x
-38 + 11x = (-6 + -1x + x2)

Solving
-38 + 11x = -6 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-38 + 6 + 11x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: -38 + 6 = -32
-32 + 11x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 11x + x = 12x
-32 + 12x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Reorder the terms:
-32 + 12x + -1x2 = -6 + 6 + -1x + x + x2 + -1x2

Combine like terms: -6 + 6 = 0
-32 + 12x + -1x2 = 0 + -1x + x + x2 + -1x2
-32 + 12x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-32 + 12x + -1x2 = 0 + x2 + -1x2
-32 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-32 + 12x + -1x2 = 0

Factor a trinomial.
(-8 + x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

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

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

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 = {8, 4}

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