3(x+2)(x-2)=3(7x+8)-12

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Solution for 3(x+2)(x-2)=3(7x+8)-12 equation: 


Simplifying
3(x + 2)(x + -2) = 3(7x + 8) + -12

Reorder the terms:
3(2 + x)(x + -2) = 3(7x + 8) + -12

Reorder the terms:
3(2 + x)(-2 + x) = 3(7x + 8) + -12

Multiply (2 + x) * (-2 + x)
3(2(-2 + x) + x(-2 + x)) = 3(7x + 8) + -12
3((-2 * 2 + x * 2) + x(-2 + x)) = 3(7x + 8) + -12
3((-4 + 2x) + x(-2 + x)) = 3(7x + 8) + -12
3(-4 + 2x + (-2 * x + x * x)) = 3(7x + 8) + -12
3(-4 + 2x + (-2x + x2)) = 3(7x + 8) + -12

Combine like terms: 2x + -2x = 0
3(-4 + 0 + x2) = 3(7x + 8) + -12
3(-4 + x2) = 3(7x + 8) + -12
(-4 * 3 + x2 * 3) = 3(7x + 8) + -12
(-12 + 3x2) = 3(7x + 8) + -12

Reorder the terms:
-12 + 3x2 = 3(8 + 7x) + -12
-12 + 3x2 = (8 * 3 + 7x * 3) + -12
-12 + 3x2 = (24 + 21x) + -12

Reorder the terms:
-12 + 3x2 = 24 + -12 + 21x

Combine like terms: 24 + -12 = 12
-12 + 3x2 = 12 + 21x

Solving
-12 + 3x2 = 12 + 21x

Solving for variable 'x'.

Reorder the terms:
-12 + -12 + -21x + 3x2 = 12 + 21x + -12 + -21x

Combine like terms: -12 + -12 = -24
-24 + -21x + 3x2 = 12 + 21x + -12 + -21x

Reorder the terms:
-24 + -21x + 3x2 = 12 + -12 + 21x + -21x

Combine like terms: 12 + -12 = 0
-24 + -21x + 3x2 = 0 + 21x + -21x
-24 + -21x + 3x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-24 + -21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -7x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

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 = {-1, 8}

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