180=(2x+8)(7x-2)

Solution for 180=(2x+8)(7x-2) equation:

Simplifying
180 = (2x + 8)(7x + -2)

Reorder the terms:
180 = (8 + 2x)(7x + -2)

Reorder the terms:
180 = (8 + 2x)(-2 + 7x)

Multiply (8 + 2x) * (-2 + 7x)
180 = (8(-2 + 7x) + 2x * (-2 + 7x))
180 = ((-2 * 8 + 7x * 8) + 2x * (-2 + 7x))
180 = ((-16 + 56x) + 2x * (-2 + 7x))
180 = (-16 + 56x + (-2 * 2x + 7x * 2x))
180 = (-16 + 56x + (-4x + 14x2))

Combine like terms: 56x + -4x = 52x
180 = (-16 + 52x + 14x2)

Solving
180 = -16 + 52x + 14x2

Solving for variable 'x'.

Combine like terms: 180 + 16 = 196
196 + -52x + -14x2 = -16 + 52x + 14x2 + 16 + -52x + -14x2

Reorder the terms:
196 + -52x + -14x2 = -16 + 16 + 52x + -52x + 14x2 + -14x2

Combine like terms: -16 + 16 = 0
196 + -52x + -14x2 = 0 + 52x + -52x + 14x2 + -14x2
196 + -52x + -14x2 = 52x + -52x + 14x2 + -14x2

Combine like terms: 52x + -52x = 0
196 + -52x + -14x2 = 0 + 14x2 + -14x2
196 + -52x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
196 + -52x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(98 + -26x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(98 + -26x + -7x2)' equal to zero and attempt to solve:

Simplifying
98 + -26x + -7x2 = 0

Solving
98 + -26x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-14 + 3.714285714x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 3.714285714x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 3.714285714x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 3.714285714x + x2 = 0 + 14
3.714285714x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
3.714285714x + x2 = 14

The x term is 3.714285714x.  Take half its coefficient (1.857142857).
Square it (3.448979591) and add it to both sides.

Add '3.448979591' to each side of the equation.
3.714285714x + 3.448979591 + x2 = 14 + 3.448979591

Reorder the terms:
3.448979591 + 3.714285714x + x2 = 14 + 3.448979591

Combine like terms: 14 + 3.448979591 = 17.448979591
3.448979591 + 3.714285714x + x2 = 17.448979591

Factor a perfect square on the left side:
(x + 1.857142857)(x + 1.857142857) = 17.448979591

Calculate the square root of the right side: 4.177197576

Break this problem into two subproblems by setting 
(x + 1.857142857) equal to 4.177197576 and -4.177197576.

Subproblem 1
x + 1.857142857 = 4.177197576

Simplifying
x + 1.857142857 = 4.177197576

Reorder the terms:
1.857142857 + x = 4.177197576

Solving
1.857142857 + x = 4.177197576

Solving for variable 'x'.

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

Add '-1.857142857' to each side of the equation.
1.857142857 + -1.857142857 + x = 4.177197576 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + x = 4.177197576 + -1.857142857
x = 4.177197576 + -1.857142857

Combine like terms: 4.177197576 + -1.857142857 = 2.320054719
x = 2.320054719

Simplifying
x = 2.320054719

Subproblem 2
x + 1.857142857 = -4.177197576

Simplifying
x + 1.857142857 = -4.177197576

Reorder the terms:
1.857142857 + x = -4.177197576

Solving
1.857142857 + x = -4.177197576

Solving for variable 'x'.

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

Add '-1.857142857' to each side of the equation.
1.857142857 + -1.857142857 + x = -4.177197576 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + x = -4.177197576 + -1.857142857
x = -4.177197576 + -1.857142857

Combine like terms: -4.177197576 + -1.857142857 = -6.034340433
x = -6.034340433

Simplifying
x = -6.034340433

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.320054719, -6.034340433}
Solution
x = {2.320054719, -6.034340433}