(400+50x)(200-x)=80000+800x-50x

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Solution for (400+50x)(200-x)=80000+800x-50x equation: 


Simplifying
(400 + 50x)(200 + -1x) = 80000 + 800x + -50x

Multiply (400 + 50x) * (200 + -1x)
(400(200 + -1x) + 50x * (200 + -1x)) = 80000 + 800x + -50x
((200 * 400 + -1x * 400) + 50x * (200 + -1x)) = 80000 + 800x + -50x
((80000 + -400x) + 50x * (200 + -1x)) = 80000 + 800x + -50x
(80000 + -400x + (200 * 50x + -1x * 50x)) = 80000 + 800x + -50x
(80000 + -400x + (10000x + -50x2)) = 80000 + 800x + -50x

Combine like terms: -400x + 10000x = 9600x
(80000 + 9600x + -50x2) = 80000 + 800x + -50x

Combine like terms: 800x + -50x = 750x
80000 + 9600x + -50x2 = 80000 + 750x

Add '-80000' to each side of the equation.
80000 + 9600x + -80000 + -50x2 = 80000 + -80000 + 750x

Reorder the terms:
80000 + -80000 + 9600x + -50x2 = 80000 + -80000 + 750x

Combine like terms: 80000 + -80000 = 0
0 + 9600x + -50x2 = 80000 + -80000 + 750x
9600x + -50x2 = 80000 + -80000 + 750x

Combine like terms: 80000 + -80000 = 0
9600x + -50x2 = 0 + 750x
9600x + -50x2 = 750x

Solving
9600x + -50x2 = 750x

Solving for variable 'x'.

Reorder the terms:
9600x + -750x + -50x2 = 750x + -750x

Combine like terms: 9600x + -750x = 8850x
8850x + -50x2 = 750x + -750x

Combine like terms: 750x + -750x = 0
8850x + -50x2 = 0

Factor out the Greatest Common Factor (GCF), '50x'.
50x(177 + -1x) = 0

Ignore the factor 50.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(177 + -1x)' equal to zero and attempt to solve:

Simplifying
177 + -1x = 0

Solving
177 + -1x = 0

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

Add '-177' to each side of the equation.
177 + -177 + -1x = 0 + -177

Combine like terms: 177 + -177 = 0
0 + -1x = 0 + -177
-1x = 0 + -177

Combine like terms: 0 + -177 = -177
-1x = -177

Divide each side by '-1'.
x = 177

Simplifying
x = 177
Solution
x = {0, 177}

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