(x+1)(4x-56)=180

Solution for (x+1)(4x-56)=180 equation:

Simplifying
(x + 1)(4x + -56) = 180

Reorder the terms:
(1 + x)(4x + -56) = 180

Reorder the terms:
(1 + x)(-56 + 4x) = 180

Multiply (1 + x) * (-56 + 4x)
(1(-56 + 4x) + x(-56 + 4x)) = 180
((-56 * 1 + 4x * 1) + x(-56 + 4x)) = 180
((-56 + 4x) + x(-56 + 4x)) = 180
(-56 + 4x + (-56 * x + 4x * x)) = 180
(-56 + 4x + (-56x + 4x2)) = 180

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

Solving
-56 + -52x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-56 + -180 + -52x + 4x2 = 180 + -180

Combine like terms: -56 + -180 = -236
-236 + -52x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-236 + -52x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-59 + -13x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-59 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-59 + -13x + x2 = 0

Solving
-59 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + -13x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + -13x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + -13x + x2 = 0 + 59
-13x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
-13x + x2 = 59

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 59 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 59 + 42.25

Combine like terms: 59 + 42.25 = 101.25
42.25 + -13x + x2 = 101.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + -6.5) equal to 10.062305899 and -10.062305899.

Subproblem 1
x + -6.5 = 10.062305899

Simplifying
x + -6.5 = 10.062305899

Reorder the terms:
-6.5 + x = 10.062305899

Solving
-6.5 + x = 10.062305899

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 10.062305899 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 10.062305899 + 6.5
x = 10.062305899 + 6.5

Combine like terms: 10.062305899 + 6.5 = 16.562305899
x = 16.562305899

Simplifying
x = 16.562305899

Subproblem 2
x + -6.5 = -10.062305899

Simplifying
x + -6.5 = -10.062305899

Reorder the terms:
-6.5 + x = -10.062305899

Solving
-6.5 + x = -10.062305899

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -10.062305899 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -10.062305899 + 6.5
x = -10.062305899 + 6.5

Combine like terms: -10.062305899 + 6.5 = -3.562305899
x = -3.562305899

Simplifying
x = -3.562305899

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.562305899, -3.562305899}
Solution
x = {16.562305899, -3.562305899}