(6x-4)(4x-16)=180

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Solution for (6x-4)(4x-16)=180 equation: 


Simplifying
(6x + -4)(4x + -16) = 180

Reorder the terms:
(-4 + 6x)(4x + -16) = 180

Reorder the terms:
(-4 + 6x)(-16 + 4x) = 180

Multiply (-4 + 6x) * (-16 + 4x)
(-4(-16 + 4x) + 6x * (-16 + 4x)) = 180
((-16 * -4 + 4x * -4) + 6x * (-16 + 4x)) = 180
((64 + -16x) + 6x * (-16 + 4x)) = 180
(64 + -16x + (-16 * 6x + 4x * 6x)) = 180
(64 + -16x + (-96x + 24x2)) = 180

Combine like terms: -16x + -96x = -112x
(64 + -112x + 24x2) = 180

Solving
64 + -112x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
64 + -180 + -112x + 24x2 = 180 + -180

Combine like terms: 64 + -180 = -116
-116 + -112x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-116 + -112x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-29 + -28x + 6x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + -28x + 6x2)' equal to zero and attempt to solve:

Simplifying
-29 + -28x + 6x2 = 0

Solving
-29 + -28x + 6x2 = 0

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

Divide each side by '6'.
-4.833333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '4.833333333' to each side of the equation.
-4.833333333 + -4.666666667x + 4.833333333 + x2 = 0 + 4.833333333

Reorder the terms:
-4.833333333 + 4.833333333 + -4.666666667x + x2 = 0 + 4.833333333

Combine like terms: -4.833333333 + 4.833333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 4.833333333
-4.666666667x + x2 = 0 + 4.833333333

Combine like terms: 0 + 4.833333333 = 4.833333333
-4.666666667x + x2 = 4.833333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 4.833333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 4.833333333 + 5.444444448

Combine like terms: 4.833333333 + 5.444444448 = 10.277777781
5.444444448 + -4.666666667x + x2 = 10.277777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 10.277777781

Calculate the square root of the right side: 3.205897344

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.205897344 and -3.205897344.


Subproblem 1
x + -2.333333334 = 3.205897344

Simplifying
x + -2.333333334 = 3.205897344

Reorder the terms:
-2.333333334 + x = 3.205897344

Solving
-2.333333334 + x = 3.205897344

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.205897344 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.205897344 + 2.333333334
x = 3.205897344 + 2.333333334

Combine like terms: 3.205897344 + 2.333333334 = 5.539230678
x = 5.539230678

Simplifying
x = 5.539230678


Subproblem 2
x + -2.333333334 = -3.205897344

Simplifying
x + -2.333333334 = -3.205897344

Reorder the terms:
-2.333333334 + x = -3.205897344

Solving
-2.333333334 + x = -3.205897344

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.205897344 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.205897344 + 2.333333334
x = -3.205897344 + 2.333333334

Combine like terms: -3.205897344 + 2.333333334 = -0.87256401
x = -0.87256401

Simplifying
x = -0.87256401


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.539230678, -0.87256401}
Solution
x = {5.539230678, -0.87256401}

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