(4x-2)(x+7)=180

Solution for (4x-2)(x+7)=180 equation:

Simplifying
(4x + -2)(x + 7) = 180

Reorder the terms:
(-2 + 4x)(x + 7) = 180

Reorder the terms:
(-2 + 4x)(7 + x) = 180

Multiply (-2 + 4x) * (7 + x)
(-2(7 + x) + 4x * (7 + x)) = 180
((7 * -2 + x * -2) + 4x * (7 + x)) = 180
((-14 + -2x) + 4x * (7 + x)) = 180
(-14 + -2x + (7 * 4x + x * 4x)) = 180
(-14 + -2x + (28x + 4x2)) = 180

Combine like terms: -2x + 28x = 26x
(-14 + 26x + 4x2) = 180

Solving
-14 + 26x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-14 + -180 + 26x + 4x2 = 180 + -180

Combine like terms: -14 + -180 = -194
-194 + 26x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-194 + 26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-97 + 13x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-97 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-97 + 13x + 2x2 = 0

Solving
-97 + 13x + 2x2 = 0

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

Divide each side by '2'.
-48.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '48.5' to each side of the equation.
-48.5 + 6.5x + 48.5 + x2 = 0 + 48.5

Reorder the terms:
-48.5 + 48.5 + 6.5x + x2 = 0 + 48.5

Combine like terms: -48.5 + 48.5 = 0.0
0.0 + 6.5x + x2 = 0 + 48.5
6.5x + x2 = 0 + 48.5

Combine like terms: 0 + 48.5 = 48.5
6.5x + x2 = 48.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 48.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 48.5 + 10.5625

Combine like terms: 48.5 + 10.5625 = 59.0625
10.5625 + 6.5x + x2 = 59.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 59.0625

Calculate the square root of the right side: 7.685213074

Break this problem into two subproblems by setting 
(x + 3.25) equal to 7.685213074 and -7.685213074.

Subproblem 1
x + 3.25 = 7.685213074

Simplifying
x + 3.25 = 7.685213074

Reorder the terms:
3.25 + x = 7.685213074

Solving
3.25 + x = 7.685213074

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 7.685213074 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 7.685213074 + -3.25
x = 7.685213074 + -3.25

Combine like terms: 7.685213074 + -3.25 = 4.435213074
x = 4.435213074

Simplifying
x = 4.435213074

Subproblem 2
x + 3.25 = -7.685213074

Simplifying
x + 3.25 = -7.685213074

Reorder the terms:
3.25 + x = -7.685213074

Solving
3.25 + x = -7.685213074

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -7.685213074 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -7.685213074 + -3.25
x = -7.685213074 + -3.25

Combine like terms: -7.685213074 + -3.25 = -10.935213074
x = -10.935213074

Simplifying
x = -10.935213074

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.435213074, -10.935213074}
Solution
x = {4.435213074, -10.935213074}