-x^2+46x-480=0

Solution for -x^2+46x-480=0 equation:

Simplifying
-1x2 + 46x + -480 = 0

Reorder the terms:
-480 + 46x + -1x2 = 0

Solving
-480 + 46x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-30 + x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-30 + x)' equal to zero and attempt to solve:

Simplifying
-30 + x = 0

Solving
-30 + x = 0

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

Add '30' to each side of the equation.
-30 + 30 + x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + x = 0 + 30
x = 0 + 30

Combine like terms: 0 + 30 = 30
x = 30

Simplifying
x = 30
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {30, 16}