(7x+13)(8x-8)=180

Solution for (7x+13)(8x-8)=180 equation:

Simplifying
(7x + 13)(8x + -8) = 180

Reorder the terms:
(13 + 7x)(8x + -8) = 180

Reorder the terms:
(13 + 7x)(-8 + 8x) = 180

Multiply (13 + 7x) * (-8 + 8x)
(13(-8 + 8x) + 7x * (-8 + 8x)) = 180
((-8 * 13 + 8x * 13) + 7x * (-8 + 8x)) = 180
((-104 + 104x) + 7x * (-8 + 8x)) = 180
(-104 + 104x + (-8 * 7x + 8x * 7x)) = 180
(-104 + 104x + (-56x + 56x2)) = 180

Combine like terms: 104x + -56x = 48x
(-104 + 48x + 56x2) = 180

Solving
-104 + 48x + 56x2 = 180

Solving for variable 'x'.

Reorder the terms:
-104 + -180 + 48x + 56x2 = 180 + -180

Combine like terms: -104 + -180 = -284
-284 + 48x + 56x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-284 + 48x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-71 + 12x + 14x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-71 + 12x + 14x2)' equal to zero and attempt to solve:

Simplifying
-71 + 12x + 14x2 = 0

Solving
-71 + 12x + 14x2 = 0

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

Divide each side by '14'.
-5.071428571 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '5.071428571' to each side of the equation.
-5.071428571 + 0.8571428571x + 5.071428571 + x2 = 0 + 5.071428571

Reorder the terms:
-5.071428571 + 5.071428571 + 0.8571428571x + x2 = 0 + 5.071428571

Combine like terms: -5.071428571 + 5.071428571 = 0.000000000
0.000000000 + 0.8571428571x + x2 = 0 + 5.071428571
0.8571428571x + x2 = 0 + 5.071428571

Combine like terms: 0 + 5.071428571 = 5.071428571
0.8571428571x + x2 = 5.071428571

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 5.071428571 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 5.071428571 + 0.1836734694

Combine like terms: 5.071428571 + 0.1836734694 = 5.2551020404
0.1836734694 + 0.8571428571x + x2 = 5.2551020404

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 5.2551020404

Calculate the square root of the right side: 2.292400934

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 2.292400934 and -2.292400934.

Subproblem 1
x + 0.4285714286 = 2.292400934

Simplifying
x + 0.4285714286 = 2.292400934

Reorder the terms:
0.4285714286 + x = 2.292400934

Solving
0.4285714286 + x = 2.292400934

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = 2.292400934 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = 2.292400934 + -0.4285714286
x = 2.292400934 + -0.4285714286

Combine like terms: 2.292400934 + -0.4285714286 = 1.8638295054
x = 1.8638295054

Simplifying
x = 1.8638295054

Subproblem 2
x + 0.4285714286 = -2.292400934

Simplifying
x + 0.4285714286 = -2.292400934

Reorder the terms:
0.4285714286 + x = -2.292400934

Solving
0.4285714286 + x = -2.292400934

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = -2.292400934 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = -2.292400934 + -0.4285714286
x = -2.292400934 + -0.4285714286

Combine like terms: -2.292400934 + -0.4285714286 = -2.7209723626
x = -2.7209723626

Simplifying
x = -2.7209723626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8638295054, -2.7209723626}
Solution
x = {1.8638295054, -2.7209723626}