(3x+2)(4x-4)=360

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Solution for (3x+2)(4x-4)=360 equation: 


Simplifying
(3x + 2)(4x + -4) = 360

Reorder the terms:
(2 + 3x)(4x + -4) = 360

Reorder the terms:
(2 + 3x)(-4 + 4x) = 360

Multiply (2 + 3x) * (-4 + 4x)
(2(-4 + 4x) + 3x * (-4 + 4x)) = 360
((-4 * 2 + 4x * 2) + 3x * (-4 + 4x)) = 360
((-8 + 8x) + 3x * (-4 + 4x)) = 360
(-8 + 8x + (-4 * 3x + 4x * 3x)) = 360
(-8 + 8x + (-12x + 12x2)) = 360

Combine like terms: 8x + -12x = -4x
(-8 + -4x + 12x2) = 360

Solving
-8 + -4x + 12x2 = 360

Solving for variable 'x'.

Reorder the terms:
-8 + -360 + -4x + 12x2 = 360 + -360

Combine like terms: -8 + -360 = -368
-368 + -4x + 12x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-368 + -4x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-92 + -1x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-92 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
-92 + -1x + 3x2 = 0

Solving
-92 + -1x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-30.66666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '30.66666667' to each side of the equation.
-30.66666667 + -0.3333333333x + 30.66666667 + x2 = 0 + 30.66666667

Reorder the terms:
-30.66666667 + 30.66666667 + -0.3333333333x + x2 = 0 + 30.66666667

Combine like terms: -30.66666667 + 30.66666667 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + 30.66666667
-0.3333333333x + x2 = 0 + 30.66666667

Combine like terms: 0 + 30.66666667 = 30.66666667
-0.3333333333x + x2 = 30.66666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 30.66666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 30.66666667 + 0.02777777779

Combine like terms: 30.66666667 + 0.02777777779 = 30.69444444779
0.02777777779 + -0.3333333333x + x2 = 30.69444444779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 30.69444444779

Calculate the square root of the right side: 5.540256713

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 5.540256713 and -5.540256713.


Subproblem 1
x + -0.1666666667 = 5.540256713

Simplifying
x + -0.1666666667 = 5.540256713

Reorder the terms:
-0.1666666667 + x = 5.540256713

Solving
-0.1666666667 + x = 5.540256713

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 5.540256713 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 5.540256713 + 0.1666666667
x = 5.540256713 + 0.1666666667

Combine like terms: 5.540256713 + 0.1666666667 = 5.7069233797
x = 5.7069233797

Simplifying
x = 5.7069233797


Subproblem 2
x + -0.1666666667 = -5.540256713

Simplifying
x + -0.1666666667 = -5.540256713

Reorder the terms:
-0.1666666667 + x = -5.540256713

Solving
-0.1666666667 + x = -5.540256713

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -5.540256713 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -5.540256713 + 0.1666666667
x = -5.540256713 + 0.1666666667

Combine like terms: -5.540256713 + 0.1666666667 = -5.3735900463
x = -5.3735900463

Simplifying
x = -5.3735900463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.7069233797, -5.3735900463}
Solution
x = {5.7069233797, -5.3735900463}

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