(x+10)(2x-10)=180

Solution for (x+10)(2x-10)=180 equation:

Simplifying
(x + 10)(2x + -10) = 180

Reorder the terms:
(10 + x)(2x + -10) = 180

Reorder the terms:
(10 + x)(-10 + 2x) = 180

Multiply (10 + x) * (-10 + 2x)
(10(-10 + 2x) + x(-10 + 2x)) = 180
((-10 * 10 + 2x * 10) + x(-10 + 2x)) = 180
((-100 + 20x) + x(-10 + 2x)) = 180
(-100 + 20x + (-10 * x + 2x * x)) = 180
(-100 + 20x + (-10x + 2x2)) = 180

Combine like terms: 20x + -10x = 10x
(-100 + 10x + 2x2) = 180

Solving
-100 + 10x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-100 + -180 + 10x + 2x2 = 180 + -180

Combine like terms: -100 + -180 = -280
-280 + 10x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-280 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-140 + 5x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-140 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-140 + 5x + x2 = 0

Solving
-140 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 5x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 5x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 5x + x2 = 0 + 140
5x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
5x + x2 = 140

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 = 140 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 140 + 6.25

Combine like terms: 140 + 6.25 = 146.25
6.25 + 5x + x2 = 146.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.093386622 and -12.093386622.

Subproblem 1
x + 2.5 = 12.093386622

Simplifying
x + 2.5 = 12.093386622

Reorder the terms:
2.5 + x = 12.093386622

Solving
2.5 + x = 12.093386622

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 = 12.093386622 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.093386622 + -2.5
x = 12.093386622 + -2.5

Combine like terms: 12.093386622 + -2.5 = 9.593386622
x = 9.593386622

Simplifying
x = 9.593386622

Subproblem 2
x + 2.5 = -12.093386622

Simplifying
x + 2.5 = -12.093386622

Reorder the terms:
2.5 + x = -12.093386622

Solving
2.5 + x = -12.093386622

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 = -12.093386622 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.093386622 + -2.5
x = -12.093386622 + -2.5

Combine like terms: -12.093386622 + -2.5 = -14.593386622
x = -14.593386622

Simplifying
x = -14.593386622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.593386622, -14.593386622}
Solution
x = {9.593386622, -14.593386622}