200x-x^2=75x+2100

Solution for 200x-x^2=75x+2100 equation:

Simplifying
200x + -1x2 = 75x + 2100

Reorder the terms:
200x + -1x2 = 2100 + 75x

Solving
200x + -1x2 = 2100 + 75x

Solving for variable 'x'.

Reorder the terms:
-2100 + 200x + -75x + -1x2 = 2100 + 75x + -2100 + -75x

Combine like terms: 200x + -75x = 125x
-2100 + 125x + -1x2 = 2100 + 75x + -2100 + -75x

Reorder the terms:
-2100 + 125x + -1x2 = 2100 + -2100 + 75x + -75x

Combine like terms: 2100 + -2100 = 0
-2100 + 125x + -1x2 = 0 + 75x + -75x
-2100 + 125x + -1x2 = 75x + -75x

Combine like terms: 75x + -75x = 0
-2100 + 125x + -1x2 = 0

Factor a trinomial.
(-105 + x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-105 + x)' equal to zero and attempt to solve:

Simplifying
-105 + x = 0

Solving
-105 + x = 0

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

Add '105' to each side of the equation.
-105 + 105 + x = 0 + 105

Combine like terms: -105 + 105 = 0
0 + x = 0 + 105
x = 0 + 105

Combine like terms: 0 + 105 = 105
x = 105

Simplifying
x = 105
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {105, 20}