-x^2+460x-24000=0

Solution for -x^2+460x-24000=0 equation:

Simplifying
-1x2 + 460x + -24000 = 0

Reorder the terms:
-24000 + 460x + -1x2 = 0

Solving
-24000 + 460x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-400 + x)(60 + -1x) = 0

Subproblem 1
Set the factor '(-400 + x)' equal to zero and attempt to solve:

Simplifying
-400 + x = 0

Solving
-400 + x = 0

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

Add '400' to each side of the equation.
-400 + 400 + x = 0 + 400

Combine like terms: -400 + 400 = 0
0 + x = 0 + 400
x = 0 + 400

Combine like terms: 0 + 400 = 400
x = 400

Simplifying
x = 400
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {400, 60}