0=9600+-200x+x^2

Solution for 0=9600+-200x+x^2 equation:

Simplifying
0 = 9600 + -200x + x2

Solving
0 = 9600 + -200x + x2

Solving for variable 'x'.

Combine like terms: 0 + -9600 = -9600
-9600 + 200x + -1x2 = 9600 + -200x + x2 + -9600 + 200x + -1x2

Reorder the terms:
-9600 + 200x + -1x2 = 9600 + -9600 + -200x + 200x + x2 + -1x2

Combine like terms: 9600 + -9600 = 0
-9600 + 200x + -1x2 = 0 + -200x + 200x + x2 + -1x2
-9600 + 200x + -1x2 = -200x + 200x + x2 + -1x2

Combine like terms: -200x + 200x = 0
-9600 + 200x + -1x2 = 0 + x2 + -1x2
-9600 + 200x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9600 + 200x + -1x2 = 0

Factor a trinomial.
(-120 + x)(80 + -1x) = 0

Subproblem 1
Set the factor '(-120 + x)' equal to zero and attempt to solve:

Simplifying
-120 + x = 0

Solving
-120 + x = 0

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

Add '120' to each side of the equation.
-120 + 120 + x = 0 + 120

Combine like terms: -120 + 120 = 0
0 + x = 0 + 120
x = 0 + 120

Combine like terms: 0 + 120 = 120
x = 120

Simplifying
x = 120
Subproblem 2
Set the factor '(80 + -1x)' equal to zero and attempt to solve:

Simplifying
80 + -1x = 0

Solving
80 + -1x = 0

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

Add '-80' to each side of the equation.
80 + -80 + -1x = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -1x = 0 + -80
-1x = 0 + -80

Combine like terms: 0 + -80 = -80
-1x = -80

Divide each side by '-1'.
x = 80

Simplifying
x = 80
Solution
x = {120, 80}