-x^2+41x-180=0

Solution for -x^2+41x-180=0 equation:

Simplifying
-1x2 + 41x + -180 = 0

Reorder the terms:
-180 + 41x + -1x2 = 0

Solving
-180 + 41x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-36 + x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-36 + x)' equal to zero and attempt to solve:

Simplifying
-36 + x = 0

Solving
-36 + x = 0

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

Add '36' to each side of the equation.
-36 + 36 + x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + x = 0 + 36
x = 0 + 36

Combine like terms: 0 + 36 = 36
x = 36

Simplifying
x = 36
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {36, 5}