(12x+4)(8x+32)=360

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Solution for (12x+4)(8x+32)=360 equation: 


Simplifying
(12x + 4)(8x + 32) = 360

Reorder the terms:
(4 + 12x)(8x + 32) = 360

Reorder the terms:
(4 + 12x)(32 + 8x) = 360

Multiply (4 + 12x) * (32 + 8x)
(4(32 + 8x) + 12x * (32 + 8x)) = 360
((32 * 4 + 8x * 4) + 12x * (32 + 8x)) = 360
((128 + 32x) + 12x * (32 + 8x)) = 360
(128 + 32x + (32 * 12x + 8x * 12x)) = 360
(128 + 32x + (384x + 96x2)) = 360

Combine like terms: 32x + 384x = 416x
(128 + 416x + 96x2) = 360

Solving
128 + 416x + 96x2 = 360

Solving for variable 'x'.

Reorder the terms:
128 + -360 + 416x + 96x2 = 360 + -360

Combine like terms: 128 + -360 = -232
-232 + 416x + 96x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-232 + 416x + 96x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-29 + 52x + 12x2) = 0

Factor a trinomial.
8((-29 + -6x)(1 + -2x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-29 + -6x)' equal to zero and attempt to solve:

Simplifying
-29 + -6x = 0

Solving
-29 + -6x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -6x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -6x = 0 + 29
-6x = 0 + 29

Combine like terms: 0 + 29 = 29
-6x = 29

Divide each side by '-6'.
x = -4.833333333

Simplifying
x = -4.833333333

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4.833333333, 0.5}

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