(2x-70)(x+30)=180

Solution for (2x-70)(x+30)=180 equation:

Simplifying
(2x + -70)(x + 30) = 180

Reorder the terms:
(-70 + 2x)(x + 30) = 180

Reorder the terms:
(-70 + 2x)(30 + x) = 180

Multiply (-70 + 2x) * (30 + x)
(-70(30 + x) + 2x * (30 + x)) = 180
((30 * -70 + x * -70) + 2x * (30 + x)) = 180
((-2100 + -70x) + 2x * (30 + x)) = 180
(-2100 + -70x + (30 * 2x + x * 2x)) = 180
(-2100 + -70x + (60x + 2x2)) = 180

Combine like terms: -70x + 60x = -10x
(-2100 + -10x + 2x2) = 180

Solving
-2100 + -10x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-2100 + -180 + -10x + 2x2 = 180 + -180

Combine like terms: -2100 + -180 = -2280
-2280 + -10x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-2280 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1140 + -5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1140 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-1140 + -5x + x2 = 0

Solving
-1140 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1140' to each side of the equation.
-1140 + -5x + 1140 + x2 = 0 + 1140

Reorder the terms:
-1140 + 1140 + -5x + x2 = 0 + 1140

Combine like terms: -1140 + 1140 = 0
0 + -5x + x2 = 0 + 1140
-5x + x2 = 0 + 1140

Combine like terms: 0 + 1140 = 1140
-5x + x2 = 1140

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 1140 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1140 + 6.25

Combine like terms: 1140 + 6.25 = 1146.25
6.25 + -5x + x2 = 1146.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1146.25

Calculate the square root of the right side: 33.856314034

Break this problem into two subproblems by setting 
(x + -2.5) equal to 33.856314034 and -33.856314034.

Subproblem 1
x + -2.5 = 33.856314034

Simplifying
x + -2.5 = 33.856314034

Reorder the terms:
-2.5 + x = 33.856314034

Solving
-2.5 + x = 33.856314034

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 33.856314034 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 33.856314034 + 2.5
x = 33.856314034 + 2.5

Combine like terms: 33.856314034 + 2.5 = 36.356314034
x = 36.356314034

Simplifying
x = 36.356314034

Subproblem 2
x + -2.5 = -33.856314034

Simplifying
x + -2.5 = -33.856314034

Reorder the terms:
-2.5 + x = -33.856314034

Solving
-2.5 + x = -33.856314034

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -33.856314034 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -33.856314034 + 2.5
x = -33.856314034 + 2.5

Combine like terms: -33.856314034 + 2.5 = -31.356314034
x = -31.356314034

Simplifying
x = -31.356314034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.356314034, -31.356314034}
Solution
x = {36.356314034, -31.356314034}