-x^2+60x-500=375

Solution for -x^2+60x-500=375 equation:

Simplifying
-1x2 + 60x + -500 = 375

Reorder the terms:
-500 + 60x + -1x2 = 375

Solving
-500 + 60x + -1x2 = 375

Solving for variable 'x'.

Reorder the terms:
-500 + -375 + 60x + -1x2 = 375 + -375

Combine like terms: -500 + -375 = -875
-875 + 60x + -1x2 = 375 + -375

Combine like terms: 375 + -375 = 0
-875 + 60x + -1x2 = 0

Factor a trinomial.
(-35 + x)(25 + -1x) = 0

Subproblem 1
Set the factor '(-35 + x)' equal to zero and attempt to solve:

Simplifying
-35 + x = 0

Solving
-35 + x = 0

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

Add '35' to each side of the equation.
-35 + 35 + x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + x = 0 + 35
x = 0 + 35

Combine like terms: 0 + 35 = 35
x = 35

Simplifying
x = 35
Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {35, 25}