(40+2x)(30+2x)=1800

Solution for (40+2x)(30+2x)=1800 equation:

Simplifying
(40 + 2x)(30 + 2x) = 1800

Multiply (40 + 2x) * (30 + 2x)
(40(30 + 2x) + 2x * (30 + 2x)) = 1800
((30 * 40 + 2x * 40) + 2x * (30 + 2x)) = 1800
((1200 + 80x) + 2x * (30 + 2x)) = 1800
(1200 + 80x + (30 * 2x + 2x * 2x)) = 1800
(1200 + 80x + (60x + 4x2)) = 1800

Combine like terms: 80x + 60x = 140x
(1200 + 140x + 4x2) = 1800

Solving
1200 + 140x + 4x2 = 1800

Solving for variable 'x'.

Reorder the terms:
1200 + -1800 + 140x + 4x2 = 1800 + -1800

Combine like terms: 1200 + -1800 = -600
-600 + 140x + 4x2 = 1800 + -1800

Combine like terms: 1800 + -1800 = 0
-600 + 140x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-150 + 35x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-150 + 35x + x2)' equal to zero and attempt to solve:

Simplifying
-150 + 35x + x2 = 0

Solving
-150 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 35x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + 35x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 35x + x2 = 0 + 150
35x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
35x + x2 = 150

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 150 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 150 + 306.25

Combine like terms: 150 + 306.25 = 456.25
306.25 + 35x + x2 = 456.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 456.25

Calculate the square root of the right side: 21.360009363

Break this problem into two subproblems by setting 
(x + 17.5) equal to 21.360009363 and -21.360009363.

Subproblem 1
x + 17.5 = 21.360009363

Simplifying
x + 17.5 = 21.360009363

Reorder the terms:
17.5 + x = 21.360009363

Solving
17.5 + x = 21.360009363

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 21.360009363 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 21.360009363 + -17.5
x = 21.360009363 + -17.5

Combine like terms: 21.360009363 + -17.5 = 3.860009363
x = 3.860009363

Simplifying
x = 3.860009363

Subproblem 2
x + 17.5 = -21.360009363

Simplifying
x + 17.5 = -21.360009363

Reorder the terms:
17.5 + x = -21.360009363

Solving
17.5 + x = -21.360009363

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -21.360009363 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -21.360009363 + -17.5
x = -21.360009363 + -17.5

Combine like terms: -21.360009363 + -17.5 = -38.860009363
x = -38.860009363

Simplifying
x = -38.860009363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.860009363, -38.860009363}
Solution
x = {3.860009363, -38.860009363}