576=8(x+3)(x+4)

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Solution for 576=8(x+3)(x+4) equation: 


Simplifying
576 = 8(x + 3)(x + 4)

Reorder the terms:
576 = 8(3 + x)(x + 4)

Reorder the terms:
576 = 8(3 + x)(4 + x)

Multiply (3 + x) * (4 + x)
576 = 8(3(4 + x) + x(4 + x))
576 = 8((4 * 3 + x * 3) + x(4 + x))
576 = 8((12 + 3x) + x(4 + x))
576 = 8(12 + 3x + (4 * x + x * x))
576 = 8(12 + 3x + (4x + x2))

Combine like terms: 3x + 4x = 7x
576 = 8(12 + 7x + x2)
576 = (12 * 8 + 7x * 8 + x2 * 8)
576 = (96 + 56x + 8x2)

Solving
576 = 96 + 56x + 8x2

Solving for variable 'x'.

Combine like terms: 576 + -96 = 480
480 + -56x + -8x2 = 96 + 56x + 8x2 + -96 + -56x + -8x2

Reorder the terms:
480 + -56x + -8x2 = 96 + -96 + 56x + -56x + 8x2 + -8x2

Combine like terms: 96 + -96 = 0
480 + -56x + -8x2 = 0 + 56x + -56x + 8x2 + -8x2
480 + -56x + -8x2 = 56x + -56x + 8x2 + -8x2

Combine like terms: 56x + -56x = 0
480 + -56x + -8x2 = 0 + 8x2 + -8x2
480 + -56x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
480 + -56x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(60 + -7x + -1x2) = 0

Factor a trinomial.
8((5 + -1x)(12 + x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {5, -12}

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