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

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

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

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

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

Multiply (3 + x) * (4 + x)
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)) = 576

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

Solving
96 + 56x + 8x2 = 576

Solving for variable 'x'.

Reorder the terms:
96 + -576 + 56x + 8x2 = 576 + -576

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

Combine like terms: 576 + -576 = 0
-480 + 56x + 8x2 = 0

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

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

Ignore the factor 8.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 5}