(x+4)(x-3)=(-x+12)(x+7)

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Solution for (x+4)(x-3)=(-x+12)(x+7) equation: 


Simplifying
(x + 4)(x + -3) = (-1x + 12)(x + 7)

Reorder the terms:
(4 + x)(x + -3) = (-1x + 12)(x + 7)

Reorder the terms:
(4 + x)(-3 + x) = (-1x + 12)(x + 7)

Multiply (4 + x) * (-3 + x)
(4(-3 + x) + x(-3 + x)) = (-1x + 12)(x + 7)
((-3 * 4 + x * 4) + x(-3 + x)) = (-1x + 12)(x + 7)
((-12 + 4x) + x(-3 + x)) = (-1x + 12)(x + 7)
(-12 + 4x + (-3 * x + x * x)) = (-1x + 12)(x + 7)
(-12 + 4x + (-3x + x2)) = (-1x + 12)(x + 7)

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) = (-1x + 12)(x + 7)

Reorder the terms:
-12 + 1x + x2 = (12 + -1x)(x + 7)

Reorder the terms:
-12 + 1x + x2 = (12 + -1x)(7 + x)

Multiply (12 + -1x) * (7 + x)
-12 + 1x + x2 = (12(7 + x) + -1x * (7 + x))
-12 + 1x + x2 = ((7 * 12 + x * 12) + -1x * (7 + x))
-12 + 1x + x2 = ((84 + 12x) + -1x * (7 + x))
-12 + 1x + x2 = (84 + 12x + (7 * -1x + x * -1x))
-12 + 1x + x2 = (84 + 12x + (-7x + -1x2))

Combine like terms: 12x + -7x = 5x
-12 + 1x + x2 = (84 + 5x + -1x2)

Solving
-12 + 1x + x2 = 84 + 5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-12 + -84 + 1x + -5x + x2 + x2 = 84 + 5x + -1x2 + -84 + -5x + x2

Combine like terms: -12 + -84 = -96
-96 + 1x + -5x + x2 + x2 = 84 + 5x + -1x2 + -84 + -5x + x2

Combine like terms: 1x + -5x = -4x
-96 + -4x + x2 + x2 = 84 + 5x + -1x2 + -84 + -5x + x2

Combine like terms: x2 + x2 = 2x2
-96 + -4x + 2x2 = 84 + 5x + -1x2 + -84 + -5x + x2

Reorder the terms:
-96 + -4x + 2x2 = 84 + -84 + 5x + -5x + -1x2 + x2

Combine like terms: 84 + -84 = 0
-96 + -4x + 2x2 = 0 + 5x + -5x + -1x2 + x2
-96 + -4x + 2x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-96 + -4x + 2x2 = 0 + -1x2 + x2
-96 + -4x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-96 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -2x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(8 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}

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