-x^2+41x-390=0

Solution for -x^2+41x-390=0 equation:

Simplifying
-1x2 + 41x + -390 = 0

Reorder the terms:
-390 + 41x + -1x2 = 0

Solving
-390 + 41x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-26 + x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-26 + x)' equal to zero and attempt to solve:

Simplifying
-26 + x = 0

Solving
-26 + x = 0

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

Add '26' to each side of the equation.
-26 + 26 + x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + x = 0 + 26
x = 0 + 26

Combine like terms: 0 + 26 = 26
x = 26

Simplifying
x = 26
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {26, 15}