4(x-8)(x+8)+4(x+8)=0

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Solution for 4(x-8)(x+8)+4(x+8)=0 equation: 


Simplifying
4(x + -8)(x + 8) + 4(x + 8) = 0

Reorder the terms:
4(-8 + x)(x + 8) + 4(x + 8) = 0

Reorder the terms:
4(-8 + x)(8 + x) + 4(x + 8) = 0

Multiply (-8 + x) * (8 + x)
4(-8(8 + x) + x(8 + x)) + 4(x + 8) = 0
4((8 * -8 + x * -8) + x(8 + x)) + 4(x + 8) = 0
4((-64 + -8x) + x(8 + x)) + 4(x + 8) = 0
4(-64 + -8x + (8 * x + x * x)) + 4(x + 8) = 0
4(-64 + -8x + (8x + x2)) + 4(x + 8) = 0

Combine like terms: -8x + 8x = 0
4(-64 + 0 + x2) + 4(x + 8) = 0
4(-64 + x2) + 4(x + 8) = 0
(-64 * 4 + x2 * 4) + 4(x + 8) = 0
(-256 + 4x2) + 4(x + 8) = 0

Reorder the terms:
-256 + 4x2 + 4(8 + x) = 0
-256 + 4x2 + (8 * 4 + x * 4) = 0
-256 + 4x2 + (32 + 4x) = 0

Reorder the terms:
-256 + 32 + 4x + 4x2 = 0

Combine like terms: -256 + 32 = -224
-224 + 4x + 4x2 = 0

Solving
-224 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-56 + x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-8, 7}

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