8(4x+3)(6x-5)=12

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Solution for 8(4x+3)(6x-5)=12 equation: 


Simplifying
8(4x + 3)(6x + -5) = 12

Reorder the terms:
8(3 + 4x)(6x + -5) = 12

Reorder the terms:
8(3 + 4x)(-5 + 6x) = 12

Multiply (3 + 4x) * (-5 + 6x)
8(3(-5 + 6x) + 4x * (-5 + 6x)) = 12
8((-5 * 3 + 6x * 3) + 4x * (-5 + 6x)) = 12
8((-15 + 18x) + 4x * (-5 + 6x)) = 12
8(-15 + 18x + (-5 * 4x + 6x * 4x)) = 12
8(-15 + 18x + (-20x + 24x2)) = 12

Combine like terms: 18x + -20x = -2x
8(-15 + -2x + 24x2) = 12
(-15 * 8 + -2x * 8 + 24x2 * 8) = 12
(-120 + -16x + 192x2) = 12

Solving
-120 + -16x + 192x2 = 12

Solving for variable 'x'.

Reorder the terms:
-120 + -12 + -16x + 192x2 = 12 + -12

Combine like terms: -120 + -12 = -132
-132 + -16x + 192x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-132 + -16x + 192x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-33 + -4x + 48x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-33 + -4x + 48x2)' equal to zero and attempt to solve:

Simplifying
-33 + -4x + 48x2 = 0

Solving
-33 + -4x + 48x2 = 0

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

Divide each side by '48'.
-0.6875 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.6875' to each side of the equation.
-0.6875 + -0.08333333333x + 0.6875 + x2 = 0 + 0.6875

Reorder the terms:
-0.6875 + 0.6875 + -0.08333333333x + x2 = 0 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + -0.08333333333x + x2 = 0 + 0.6875
-0.08333333333x + x2 = 0 + 0.6875

Combine like terms: 0 + 0.6875 = 0.6875
-0.08333333333x + x2 = 0.6875

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 0.6875 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 0.6875 + 0.001736111111

Combine like terms: 0.6875 + 0.001736111111 = 0.689236111111
0.001736111111 + -0.08333333333x + x2 = 0.689236111111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 0.689236111111

Calculate the square root of the right side: 0.830202452

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 0.830202452 and -0.830202452.


Subproblem 1
x + -0.04166666667 = 0.830202452

Simplifying
x + -0.04166666667 = 0.830202452

Reorder the terms:
-0.04166666667 + x = 0.830202452

Solving
-0.04166666667 + x = 0.830202452

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 0.830202452 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 0.830202452 + 0.04166666667
x = 0.830202452 + 0.04166666667

Combine like terms: 0.830202452 + 0.04166666667 = 0.87186911867
x = 0.87186911867

Simplifying
x = 0.87186911867


Subproblem 2
x + -0.04166666667 = -0.830202452

Simplifying
x + -0.04166666667 = -0.830202452

Reorder the terms:
-0.04166666667 + x = -0.830202452

Solving
-0.04166666667 + x = -0.830202452

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -0.830202452 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -0.830202452 + 0.04166666667
x = -0.830202452 + 0.04166666667

Combine like terms: -0.830202452 + 0.04166666667 = -0.78853578533
x = -0.78853578533

Simplifying
x = -0.78853578533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.87186911867, -0.78853578533}
Solution
x = {0.87186911867, -0.78853578533}

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