2(x+25)(2x-30)=180

Solution for 2(x+25)(2x-30)=180 equation:

Simplifying
2(x + 25)(2x + -30) = 180

Reorder the terms:
2(25 + x)(2x + -30) = 180

Reorder the terms:
2(25 + x)(-30 + 2x) = 180

Multiply (25 + x) * (-30 + 2x)
2(25(-30 + 2x) + x(-30 + 2x)) = 180
2((-30 * 25 + 2x * 25) + x(-30 + 2x)) = 180
2((-750 + 50x) + x(-30 + 2x)) = 180
2(-750 + 50x + (-30 * x + 2x * x)) = 180
2(-750 + 50x + (-30x + 2x2)) = 180

Combine like terms: 50x + -30x = 20x
2(-750 + 20x + 2x2) = 180
(-750 * 2 + 20x * 2 + 2x2 * 2) = 180
(-1500 + 40x + 4x2) = 180

Solving
-1500 + 40x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-1500 + -180 + 40x + 4x2 = 180 + -180

Combine like terms: -1500 + -180 = -1680
-1680 + 40x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-1680 + 40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-420 + 10x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-420 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-420 + 10x + x2 = 0

Solving
-420 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '420' to each side of the equation.
-420 + 10x + 420 + x2 = 0 + 420

Reorder the terms:
-420 + 420 + 10x + x2 = 0 + 420

Combine like terms: -420 + 420 = 0
0 + 10x + x2 = 0 + 420
10x + x2 = 0 + 420

Combine like terms: 0 + 420 = 420
10x + x2 = 420

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 420 + 25

Reorder the terms:
25 + 10x + x2 = 420 + 25

Combine like terms: 420 + 25 = 445
25 + 10x + x2 = 445

Factor a perfect square on the left side:
(x + 5)(x + 5) = 445

Calculate the square root of the right side: 21.09502311

Break this problem into two subproblems by setting 
(x + 5) equal to 21.09502311 and -21.09502311.

Subproblem 1
x + 5 = 21.09502311

Simplifying
x + 5 = 21.09502311

Reorder the terms:
5 + x = 21.09502311

Solving
5 + x = 21.09502311

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 21.09502311 + -5

Combine like terms: 5 + -5 = 0
0 + x = 21.09502311 + -5
x = 21.09502311 + -5

Combine like terms: 21.09502311 + -5 = 16.09502311
x = 16.09502311

Simplifying
x = 16.09502311

Subproblem 2
x + 5 = -21.09502311

Simplifying
x + 5 = -21.09502311

Reorder the terms:
5 + x = -21.09502311

Solving
5 + x = -21.09502311

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -21.09502311 + -5

Combine like terms: 5 + -5 = 0
0 + x = -21.09502311 + -5
x = -21.09502311 + -5

Combine like terms: -21.09502311 + -5 = -26.09502311
x = -26.09502311

Simplifying
x = -26.09502311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.09502311, -26.09502311}
Solution
x = {16.09502311, -26.09502311}