2400=(40+2x)(30+2x)

Solution for 2400=(40+2x)(30+2x) equation:

Simplifying
2400 = (40 + 2x)(30 + 2x)

Multiply (40 + 2x) * (30 + 2x)
2400 = (40(30 + 2x) + 2x * (30 + 2x))
2400 = ((30 * 40 + 2x * 40) + 2x * (30 + 2x))
2400 = ((1200 + 80x) + 2x * (30 + 2x))
2400 = (1200 + 80x + (30 * 2x + 2x * 2x))
2400 = (1200 + 80x + (60x + 4x2))

Combine like terms: 80x + 60x = 140x
2400 = (1200 + 140x + 4x2)

Solving
2400 = 1200 + 140x + 4x2

Solving for variable 'x'.

Combine like terms: 2400 + -1200 = 1200
1200 + -140x + -4x2 = 1200 + 140x + 4x2 + -1200 + -140x + -4x2

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

Combine like terms: 1200 + -1200 = 0
1200 + -140x + -4x2 = 0 + 140x + -140x + 4x2 + -4x2
1200 + -140x + -4x2 = 140x + -140x + 4x2 + -4x2

Combine like terms: 140x + -140x = 0
1200 + -140x + -4x2 = 0 + 4x2 + -4x2
1200 + -140x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
1200 + -140x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(300 + -35x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(300 + -35x + -1x2)' equal to zero and attempt to solve:

Simplifying
300 + -35x + -1x2 = 0

Solving
300 + -35x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-300 + 35x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 35x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 35x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 35x + x2 = 0 + 300
35x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
35x + x2 = 300

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 = 300 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 300 + 306.25

Combine like terms: 300 + 306.25 = 606.25
306.25 + 35x + x2 = 606.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + 17.5) equal to 24.622144504 and -24.622144504.

Subproblem 1
x + 17.5 = 24.622144504

Simplifying
x + 17.5 = 24.622144504

Reorder the terms:
17.5 + x = 24.622144504

Solving
17.5 + x = 24.622144504

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 = 24.622144504 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 24.622144504 + -17.5
x = 24.622144504 + -17.5

Combine like terms: 24.622144504 + -17.5 = 7.122144504
x = 7.122144504

Simplifying
x = 7.122144504

Subproblem 2
x + 17.5 = -24.622144504

Simplifying
x + 17.5 = -24.622144504

Reorder the terms:
17.5 + x = -24.622144504

Solving
17.5 + x = -24.622144504

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 = -24.622144504 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -24.622144504 + -17.5
x = -24.622144504 + -17.5

Combine like terms: -24.622144504 + -17.5 = -42.122144504
x = -42.122144504

Simplifying
x = -42.122144504

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.122144504, -42.122144504}
Solution
x = {7.122144504, -42.122144504}