-x^2+57x-540=0

Solution for -x^2+57x-540=0 equation:

Simplifying
-1x2 + 57x + -540 = 0

Reorder the terms:
-540 + 57x + -1x2 = 0

Solving
-540 + 57x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-45 + x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-45 + x)' equal to zero and attempt to solve:

Simplifying
-45 + x = 0

Solving
-45 + x = 0

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

Add '45' to each side of the equation.
-45 + 45 + x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + x = 0 + 45
x = 0 + 45

Combine like terms: 0 + 45 = 45
x = 45

Simplifying
x = 45
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {45, 12}