(x-4)(x-3)-12=2(x+1)(x-7)

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Solution for (x-4)(x-3)-12=2(x+1)(x-7) equation: 


Simplifying
(x + -4)(x + -3) + -12 = 2(x + 1)(x + -7)

Reorder the terms:
(-4 + x)(x + -3) + -12 = 2(x + 1)(x + -7)

Reorder the terms:
(-4 + x)(-3 + x) + -12 = 2(x + 1)(x + -7)

Multiply (-4 + x) * (-3 + x)
(-4(-3 + x) + x(-3 + x)) + -12 = 2(x + 1)(x + -7)
((-3 * -4 + x * -4) + x(-3 + x)) + -12 = 2(x + 1)(x + -7)
((12 + -4x) + x(-3 + x)) + -12 = 2(x + 1)(x + -7)
(12 + -4x + (-3 * x + x * x)) + -12 = 2(x + 1)(x + -7)
(12 + -4x + (-3x + x2)) + -12 = 2(x + 1)(x + -7)

Combine like terms: -4x + -3x = -7x
(12 + -7x + x2) + -12 = 2(x + 1)(x + -7)

Reorder the terms:
12 + -12 + -7x + x2 = 2(x + 1)(x + -7)

Combine like terms: 12 + -12 = 0
0 + -7x + x2 = 2(x + 1)(x + -7)
-7x + x2 = 2(x + 1)(x + -7)

Reorder the terms:
-7x + x2 = 2(1 + x)(x + -7)

Reorder the terms:
-7x + x2 = 2(1 + x)(-7 + x)

Multiply (1 + x) * (-7 + x)
-7x + x2 = 2(1(-7 + x) + x(-7 + x))
-7x + x2 = 2((-7 * 1 + x * 1) + x(-7 + x))
-7x + x2 = 2((-7 + 1x) + x(-7 + x))
-7x + x2 = 2(-7 + 1x + (-7 * x + x * x))
-7x + x2 = 2(-7 + 1x + (-7x + x2))

Combine like terms: 1x + -7x = -6x
-7x + x2 = 2(-7 + -6x + x2)
-7x + x2 = (-7 * 2 + -6x * 2 + x2 * 2)
-7x + x2 = (-14 + -12x + 2x2)

Solving
-7x + x2 = -14 + -12x + 2x2

Solving for variable 'x'.

Reorder the terms:
14 + -7x + 12x + x2 + -2x2 = -14 + -12x + 2x2 + 14 + 12x + -2x2

Combine like terms: -7x + 12x = 5x
14 + 5x + x2 + -2x2 = -14 + -12x + 2x2 + 14 + 12x + -2x2

Combine like terms: x2 + -2x2 = -1x2
14 + 5x + -1x2 = -14 + -12x + 2x2 + 14 + 12x + -2x2

Reorder the terms:
14 + 5x + -1x2 = -14 + 14 + -12x + 12x + 2x2 + -2x2

Combine like terms: -14 + 14 = 0
14 + 5x + -1x2 = 0 + -12x + 12x + 2x2 + -2x2
14 + 5x + -1x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
14 + 5x + -1x2 = 0 + 2x2 + -2x2
14 + 5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
14 + 5x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(2 + x) = 0


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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {7, -2}

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