(6x+4)(2x-16)=180

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Solution for (6x+4)(2x-16)=180 equation: 


Simplifying
(6x + 4)(2x + -16) = 180

Reorder the terms:
(4 + 6x)(2x + -16) = 180

Reorder the terms:
(4 + 6x)(-16 + 2x) = 180

Multiply (4 + 6x) * (-16 + 2x)
(4(-16 + 2x) + 6x * (-16 + 2x)) = 180
((-16 * 4 + 2x * 4) + 6x * (-16 + 2x)) = 180
((-64 + 8x) + 6x * (-16 + 2x)) = 180
(-64 + 8x + (-16 * 6x + 2x * 6x)) = 180
(-64 + 8x + (-96x + 12x2)) = 180

Combine like terms: 8x + -96x = -88x
(-64 + -88x + 12x2) = 180

Solving
-64 + -88x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-64 + -180 + -88x + 12x2 = 180 + -180

Combine like terms: -64 + -180 = -244
-244 + -88x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-244 + -88x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-61 + -22x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-61 + -22x + 3x2)' equal to zero and attempt to solve:

Simplifying
-61 + -22x + 3x2 = 0

Solving
-61 + -22x + 3x2 = 0

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

Divide each side by '3'.
-20.33333333 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '20.33333333' to each side of the equation.
-20.33333333 + -7.333333333x + 20.33333333 + x2 = 0 + 20.33333333

Reorder the terms:
-20.33333333 + 20.33333333 + -7.333333333x + x2 = 0 + 20.33333333

Combine like terms: -20.33333333 + 20.33333333 = 0.00000000
0.00000000 + -7.333333333x + x2 = 0 + 20.33333333
-7.333333333x + x2 = 0 + 20.33333333

Combine like terms: 0 + 20.33333333 = 20.33333333
-7.333333333x + x2 = 20.33333333

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 20.33333333 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 20.33333333 + 13.44444445

Combine like terms: 20.33333333 + 13.44444445 = 33.77777778
13.44444445 + -7.333333333x + x2 = 33.77777778

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 33.77777778

Calculate the square root of the right side: 5.811865258

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 5.811865258 and -5.811865258.


Subproblem 1
x + -3.666666667 = 5.811865258

Simplifying
x + -3.666666667 = 5.811865258

Reorder the terms:
-3.666666667 + x = 5.811865258

Solving
-3.666666667 + x = 5.811865258

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 5.811865258 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 5.811865258 + 3.666666667
x = 5.811865258 + 3.666666667

Combine like terms: 5.811865258 + 3.666666667 = 9.478531925
x = 9.478531925

Simplifying
x = 9.478531925


Subproblem 2
x + -3.666666667 = -5.811865258

Simplifying
x + -3.666666667 = -5.811865258

Reorder the terms:
-3.666666667 + x = -5.811865258

Solving
-3.666666667 + x = -5.811865258

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -5.811865258 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -5.811865258 + 3.666666667
x = -5.811865258 + 3.666666667

Combine like terms: -5.811865258 + 3.666666667 = -2.145198591
x = -2.145198591

Simplifying
x = -2.145198591


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.478531925, -2.145198591}
Solution
x = {9.478531925, -2.145198591}

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