(4x-16)(5x+7)=180

Solution for (4x-16)(5x+7)=180 equation:

Simplifying
(4x + -16)(5x + 7) = 180

Reorder the terms:
(-16 + 4x)(5x + 7) = 180

Reorder the terms:
(-16 + 4x)(7 + 5x) = 180

Multiply (-16 + 4x) * (7 + 5x)
(-16(7 + 5x) + 4x * (7 + 5x)) = 180
((7 * -16 + 5x * -16) + 4x * (7 + 5x)) = 180
((-112 + -80x) + 4x * (7 + 5x)) = 180
(-112 + -80x + (7 * 4x + 5x * 4x)) = 180
(-112 + -80x + (28x + 20x2)) = 180

Combine like terms: -80x + 28x = -52x
(-112 + -52x + 20x2) = 180

Solving
-112 + -52x + 20x2 = 180

Solving for variable 'x'.

Reorder the terms:
-112 + -180 + -52x + 20x2 = 180 + -180

Combine like terms: -112 + -180 = -292
-292 + -52x + 20x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-292 + -52x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-73 + -13x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-73 + -13x + 5x2)' equal to zero and attempt to solve:

Simplifying
-73 + -13x + 5x2 = 0

Solving
-73 + -13x + 5x2 = 0

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

Divide each side by '5'.
-14.6 + -2.6x + x2 = 0

Move the constant term to the right:

Add '14.6' to each side of the equation.
-14.6 + -2.6x + 14.6 + x2 = 0 + 14.6

Reorder the terms:
-14.6 + 14.6 + -2.6x + x2 = 0 + 14.6

Combine like terms: -14.6 + 14.6 = 0.0
0.0 + -2.6x + x2 = 0 + 14.6
-2.6x + x2 = 0 + 14.6

Combine like terms: 0 + 14.6 = 14.6
-2.6x + x2 = 14.6

The x term is -2.6x.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6x + 1.69 + x2 = 14.6 + 1.69

Reorder the terms:
1.69 + -2.6x + x2 = 14.6 + 1.69

Combine like terms: 14.6 + 1.69 = 16.29
1.69 + -2.6x + x2 = 16.29

Factor a perfect square on the left side:
(x + -1.3)(x + -1.3) = 16.29

Calculate the square root of the right side: 4.036087214

Break this problem into two subproblems by setting 
(x + -1.3) equal to 4.036087214 and -4.036087214.

Subproblem 1
x + -1.3 = 4.036087214

Simplifying
x + -1.3 = 4.036087214

Reorder the terms:
-1.3 + x = 4.036087214

Solving
-1.3 + x = 4.036087214

Solving for variable 'x'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + x = 4.036087214 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + x = 4.036087214 + 1.3
x = 4.036087214 + 1.3

Combine like terms: 4.036087214 + 1.3 = 5.336087214
x = 5.336087214

Simplifying
x = 5.336087214

Subproblem 2
x + -1.3 = -4.036087214

Simplifying
x + -1.3 = -4.036087214

Reorder the terms:
-1.3 + x = -4.036087214

Solving
-1.3 + x = -4.036087214

Solving for variable 'x'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + x = -4.036087214 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + x = -4.036087214 + 1.3
x = -4.036087214 + 1.3

Combine like terms: -4.036087214 + 1.3 = -2.736087214
x = -2.736087214

Simplifying
x = -2.736087214

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.336087214, -2.736087214}
Solution
x = {5.336087214, -2.736087214}