12(x-4)-(x+2)=(x+2)(x-4)

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Solution for 12(x-4)-(x+2)=(x+2)(x-4) equation:


Simplifying
12(x + -4) + -1(x + 2) = (x + 2)(x + -4)

Reorder the terms:
12(-4 + x) + -1(x + 2) = (x + 2)(x + -4)
(-4 * 12 + x * 12) + -1(x + 2) = (x + 2)(x + -4)
(-48 + 12x) + -1(x + 2) = (x + 2)(x + -4)

Reorder the terms:
-48 + 12x + -1(2 + x) = (x + 2)(x + -4)
-48 + 12x + (2 * -1 + x * -1) = (x + 2)(x + -4)
-48 + 12x + (-2 + -1x) = (x + 2)(x + -4)

Reorder the terms:
-48 + -2 + 12x + -1x = (x + 2)(x + -4)

Combine like terms: -48 + -2 = -50
-50 + 12x + -1x = (x + 2)(x + -4)

Combine like terms: 12x + -1x = 11x
-50 + 11x = (x + 2)(x + -4)

Reorder the terms:
-50 + 11x = (2 + x)(x + -4)

Reorder the terms:
-50 + 11x = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-50 + 11x = (2(-4 + x) + x(-4 + x))
-50 + 11x = ((-4 * 2 + x * 2) + x(-4 + x))
-50 + 11x = ((-8 + 2x) + x(-4 + x))
-50 + 11x = (-8 + 2x + (-4 * x + x * x))
-50 + 11x = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-50 + 11x = (-8 + -2x + x2)

Solving
-50 + 11x = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-50 + 8 + 11x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -50 + 8 = -42
-42 + 11x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 11x + 2x = 13x
-42 + 13x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
-42 + 13x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
-42 + 13x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-42 + 13x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-42 + 13x + -1x2 = 0 + x2 + -1x2
-42 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 13x + -1x2 = 0

Factor a trinomial.
(-7 + x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {7, 6}

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