2((300*75)+(240*75))=((240*75)+x)((300*75)+x)

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Solution for 2((300*75)+(240*75))=((240*75)+x)((300*75)+x) equation: 


Simplifying
2((300 * 75) + (240 * 75)) = ((240 * 75) + x)((300 * 75) + x)

Multiply 300 * 75
2((22500) + (240 * 75)) = ((240 * 75) + x)((300 * 75) + x)
2(22500 + (240 * 75)) = ((240 * 75) + x)((300 * 75) + x)

Multiply 240 * 75
2(22500 + (18000)) = ((240 * 75) + x)((300 * 75) + x)
2(22500 + 18000) = ((240 * 75) + x)((300 * 75) + x)

Combine like terms: 22500 + 18000 = 40500
2(40500) = ((240 * 75) + x)((300 * 75) + x)

Multiply 2 * 40500
81000 = ((240 * 75) + x)((300 * 75) + x)

Multiply 240 * 75
81000 = ((18000) + x)((300 * 75) + x)
81000 = (18000 + x)((300 * 75) + x)

Multiply 300 * 75
81000 = (18000 + x)((22500) + x)
81000 = (18000 + x)(22500 + x)

Multiply (18000 + x) * (22500 + x)
81000 = (18000(22500 + x) + x(22500 + x))
81000 = ((22500 * 18000 + x * 18000) + x(22500 + x))
81000 = ((405000000 + 18000x) + x(22500 + x))
81000 = (405000000 + 18000x + (22500 * x + x * x))
81000 = (405000000 + 18000x + (22500x + x2))

Combine like terms: 18000x + 22500x = 40500x
81000 = (405000000 + 40500x + x2)

Solving
81000 = 405000000 + 40500x + x2

Solving for variable 'x'.

Combine like terms: 81000 + -405000000 = -404919000
-404919000 + -40500x + -1x2 = 405000000 + 40500x + x2 + -405000000 + -40500x + -1x2

Reorder the terms:
-404919000 + -40500x + -1x2 = 405000000 + -405000000 + 40500x + -40500x + x2 + -1x2

Combine like terms: 405000000 + -405000000 = 0
-404919000 + -40500x + -1x2 = 0 + 40500x + -40500x + x2 + -1x2
-404919000 + -40500x + -1x2 = 40500x + -40500x + x2 + -1x2

Combine like terms: 40500x + -40500x = 0
-404919000 + -40500x + -1x2 = 0 + x2 + -1x2
-404919000 + -40500x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-404919000 + -40500x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(404919000 + 40500x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(404919000 + 40500x + x2)' equal to zero and attempt to solve:

Simplifying
404919000 + 40500x + x2 = 0

Solving
404919000 + 40500x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-404919000' to each side of the equation.
404919000 + 40500x + -404919000 + x2 = 0 + -404919000

Reorder the terms:
404919000 + -404919000 + 40500x + x2 = 0 + -404919000

Combine like terms: 404919000 + -404919000 = 0
0 + 40500x + x2 = 0 + -404919000
40500x + x2 = 0 + -404919000

Combine like terms: 0 + -404919000 = -404919000
40500x + x2 = -404919000

The x term is 40500x.  Take half its coefficient (20250).
Square it (410062500) and add it to both sides.

Add '410062500' to each side of the equation.
40500x + 410062500 + x2 = -404919000 + 410062500

Reorder the terms:
410062500 + 40500x + x2 = -404919000 + 410062500

Combine like terms: -404919000 + 410062500 = 5143500
410062500 + 40500x + x2 = 5143500

Factor a perfect square on the left side:
(x + 20250)(x + 20250) = 5143500

Calculate the square root of the right side: 2267.928570304

Break this problem into two subproblems by setting 
(x + 20250) equal to 2267.928570304 and -2267.928570304.


Subproblem 1
x + 20250 = 2267.928570304

Simplifying
x + 20250 = 2267.928570304

Reorder the terms:
20250 + x = 2267.928570304

Solving
20250 + x = 2267.928570304

Solving for variable 'x'.

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

Add '-20250' to each side of the equation.
20250 + -20250 + x = 2267.928570304 + -20250

Combine like terms: 20250 + -20250 = 0
0 + x = 2267.928570304 + -20250
x = 2267.928570304 + -20250

Combine like terms: 2267.928570304 + -20250 = -17982.071429696
x = -17982.071429696

Simplifying
x = -17982.071429696


Subproblem 2
x + 20250 = -2267.928570304

Simplifying
x + 20250 = -2267.928570304

Reorder the terms:
20250 + x = -2267.928570304

Solving
20250 + x = -2267.928570304

Solving for variable 'x'.

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

Add '-20250' to each side of the equation.
20250 + -20250 + x = -2267.928570304 + -20250

Combine like terms: 20250 + -20250 = 0
0 + x = -2267.928570304 + -20250
x = -2267.928570304 + -20250

Combine like terms: -2267.928570304 + -20250 = -22517.928570304
x = -22517.928570304

Simplifying
x = -22517.928570304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-17982.071429696, -22517.928570304}
Solution
x = {-17982.071429696, -22517.928570304}

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