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

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


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

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

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

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

Combine like terms: 96x + -4x = 92x
(-64 + 92x + 6x2) = 180

Solving
-64 + 92x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-64 + -180 + 92x + 6x2 = 180 + -180

Combine like terms: -64 + -180 = -244
-244 + 92x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-244 + 92x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-122 + 46x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-122 + 46x + 3x2)' equal to zero and attempt to solve:

Simplifying
-122 + 46x + 3x2 = 0

Solving
-122 + 46x + 3x2 = 0

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

Divide each side by '3'.
-40.66666667 + 15.33333333x + x2 = 0

Move the constant term to the right:

Add '40.66666667' to each side of the equation.
-40.66666667 + 15.33333333x + 40.66666667 + x2 = 0 + 40.66666667

Reorder the terms:
-40.66666667 + 40.66666667 + 15.33333333x + x2 = 0 + 40.66666667

Combine like terms: -40.66666667 + 40.66666667 = 0.00000000
0.00000000 + 15.33333333x + x2 = 0 + 40.66666667
15.33333333x + x2 = 0 + 40.66666667

Combine like terms: 0 + 40.66666667 = 40.66666667
15.33333333x + x2 = 40.66666667

The x term is 15.33333333x.  Take half its coefficient (7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
15.33333333x + 58.77777775 + x2 = 40.66666667 + 58.77777775

Reorder the terms:
58.77777775 + 15.33333333x + x2 = 40.66666667 + 58.77777775

Combine like terms: 40.66666667 + 58.77777775 = 99.44444442
58.77777775 + 15.33333333x + x2 = 99.44444442

Factor a perfect square on the left side:
(x + 7.666666665)(x + 7.666666665) = 99.44444442

Calculate the square root of the right side: 9.972183533

Break this problem into two subproblems by setting 
(x + 7.666666665) equal to 9.972183533 and -9.972183533.


Subproblem 1
x + 7.666666665 = 9.972183533

Simplifying
x + 7.666666665 = 9.972183533

Reorder the terms:
7.666666665 + x = 9.972183533

Solving
7.666666665 + x = 9.972183533

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = 9.972183533 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = 9.972183533 + -7.666666665
x = 9.972183533 + -7.666666665

Combine like terms: 9.972183533 + -7.666666665 = 2.305516868
x = 2.305516868

Simplifying
x = 2.305516868


Subproblem 2
x + 7.666666665 = -9.972183533

Simplifying
x + 7.666666665 = -9.972183533

Reorder the terms:
7.666666665 + x = -9.972183533

Solving
7.666666665 + x = -9.972183533

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = -9.972183533 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = -9.972183533 + -7.666666665
x = -9.972183533 + -7.666666665

Combine like terms: -9.972183533 + -7.666666665 = -17.638850198
x = -17.638850198

Simplifying
x = -17.638850198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.305516868, -17.638850198}
Solution
x = {2.305516868, -17.638850198}

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