(4x-35)(x+7)=180

Solution for (4x-35)(x+7)=180 equation:

Simplifying
(4x + -35)(x + 7) = 180

Reorder the terms:
(-35 + 4x)(x + 7) = 180

Reorder the terms:
(-35 + 4x)(7 + x) = 180

Multiply (-35 + 4x) * (7 + x)
(-35(7 + x) + 4x * (7 + x)) = 180
((7 * -35 + x * -35) + 4x * (7 + x)) = 180
((-245 + -35x) + 4x * (7 + x)) = 180
(-245 + -35x + (7 * 4x + x * 4x)) = 180
(-245 + -35x + (28x + 4x2)) = 180

Combine like terms: -35x + 28x = -7x
(-245 + -7x + 4x2) = 180

Solving
-245 + -7x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-245 + -180 + -7x + 4x2 = 180 + -180

Combine like terms: -245 + -180 = -425
-425 + -7x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-425 + -7x + 4x2 = 0

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

Divide each side by '4'.
-106.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '106.25' to each side of the equation.
-106.25 + -1.75x + 106.25 + x2 = 0 + 106.25

Reorder the terms:
-106.25 + 106.25 + -1.75x + x2 = 0 + 106.25

Combine like terms: -106.25 + 106.25 = 0.00
0.00 + -1.75x + x2 = 0 + 106.25
-1.75x + x2 = 0 + 106.25

Combine like terms: 0 + 106.25 = 106.25
-1.75x + x2 = 106.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 106.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 106.25 + 0.765625

Combine like terms: 106.25 + 0.765625 = 107.015625
0.765625 + -1.75x + x2 = 107.015625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 107.015625

Calculate the square root of the right side: 10.344835668

Break this problem into two subproblems by setting 
(x + -0.875) equal to 10.344835668 and -10.344835668.

Subproblem 1
x + -0.875 = 10.344835668

Simplifying
x + -0.875 = 10.344835668

Reorder the terms:
-0.875 + x = 10.344835668

Solving
-0.875 + x = 10.344835668

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 10.344835668 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 10.344835668 + 0.875
x = 10.344835668 + 0.875

Combine like terms: 10.344835668 + 0.875 = 11.219835668
x = 11.219835668

Simplifying
x = 11.219835668

Subproblem 2
x + -0.875 = -10.344835668

Simplifying
x + -0.875 = -10.344835668

Reorder the terms:
-0.875 + x = -10.344835668

Solving
-0.875 + x = -10.344835668

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -10.344835668 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -10.344835668 + 0.875
x = -10.344835668 + 0.875

Combine like terms: -10.344835668 + 0.875 = -9.469835668
x = -9.469835668

Simplifying
x = -9.469835668

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.219835668, -9.469835668}