(6x-4)(4x-16)=90

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Solution for (6x-4)(4x-16)=90 equation: 


Simplifying
(6x + -4)(4x + -16) = 90

Reorder the terms:
(-4 + 6x)(4x + -16) = 90

Reorder the terms:
(-4 + 6x)(-16 + 4x) = 90

Multiply (-4 + 6x) * (-16 + 4x)
(-4(-16 + 4x) + 6x * (-16 + 4x)) = 90
((-16 * -4 + 4x * -4) + 6x * (-16 + 4x)) = 90
((64 + -16x) + 6x * (-16 + 4x)) = 90
(64 + -16x + (-16 * 6x + 4x * 6x)) = 90
(64 + -16x + (-96x + 24x2)) = 90

Combine like terms: -16x + -96x = -112x
(64 + -112x + 24x2) = 90

Solving
64 + -112x + 24x2 = 90

Solving for variable 'x'.

Reorder the terms:
64 + -90 + -112x + 24x2 = 90 + -90

Combine like terms: 64 + -90 = -26
-26 + -112x + 24x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-26 + -112x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -56x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + -56x + 12x2)' equal to zero and attempt to solve:

Simplifying
-13 + -56x + 12x2 = 0

Solving
-13 + -56x + 12x2 = 0

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

Divide each side by '12'.
-1.083333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '1.083333333' to each side of the equation.
-1.083333333 + -4.666666667x + 1.083333333 + x2 = 0 + 1.083333333

Reorder the terms:
-1.083333333 + 1.083333333 + -4.666666667x + x2 = 0 + 1.083333333

Combine like terms: -1.083333333 + 1.083333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 1.083333333
-4.666666667x + x2 = 0 + 1.083333333

Combine like terms: 0 + 1.083333333 = 1.083333333
-4.666666667x + x2 = 1.083333333

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 = 1.083333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 1.083333333 + 5.444444448

Combine like terms: 1.083333333 + 5.444444448 = 6.527777781
5.444444448 + -4.666666667x + x2 = 6.527777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.527777781

Calculate the square root of the right side: 2.55495162

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.55495162 and -2.55495162.


Subproblem 1
x + -2.333333334 = 2.55495162

Simplifying
x + -2.333333334 = 2.55495162

Reorder the terms:
-2.333333334 + x = 2.55495162

Solving
-2.333333334 + x = 2.55495162

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 = 2.55495162 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.55495162 + 2.333333334
x = 2.55495162 + 2.333333334

Combine like terms: 2.55495162 + 2.333333334 = 4.888284954
x = 4.888284954

Simplifying
x = 4.888284954


Subproblem 2
x + -2.333333334 = -2.55495162

Simplifying
x + -2.333333334 = -2.55495162

Reorder the terms:
-2.333333334 + x = -2.55495162

Solving
-2.333333334 + x = -2.55495162

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 = -2.55495162 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.55495162 + 2.333333334
x = -2.55495162 + 2.333333334

Combine like terms: -2.55495162 + 2.333333334 = -0.221618286
x = -0.221618286

Simplifying
x = -0.221618286


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.888284954, -0.221618286}
Solution
x = {4.888284954, -0.221618286}

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