500x-x^2=60000

Solution for 500x-x^2=60000 equation:

Simplifying
500x + -1x2 = 60000

Solving
500x + -1x2 = 60000

Solving for variable 'x'.

Reorder the terms:
-60000 + 500x + -1x2 = 60000 + -60000

Combine like terms: 60000 + -60000 = 0
-60000 + 500x + -1x2 = 0

Factor a trinomial.
(-300 + x)(200 + -1x) = 0

Subproblem 1
Set the factor '(-300 + x)' equal to zero and attempt to solve:

Simplifying
-300 + x = 0

Solving
-300 + x = 0

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

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

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

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

Simplifying
x = 300
Subproblem 2
Set the factor '(200 + -1x)' equal to zero and attempt to solve:

Simplifying
200 + -1x = 0

Solving
200 + -1x = 0

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

Add '-200' to each side of the equation.
200 + -200 + -1x = 0 + -200

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

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

Divide each side by '-1'.
x = 200

Simplifying
x = 200
Solution
x = {300, 200}