0=-2x^2+106x-480

Solution for 0=-2x^2+106x-480 equation:

Simplifying
0 = -2x2 + 106x + -480

Reorder the terms:
0 = -480 + 106x + -2x2

Solving
0 = -480 + 106x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 480 = 480
480 + -106x + 2x2 = -480 + 106x + -2x2 + 480 + -106x + 2x2

Reorder the terms:
480 + -106x + 2x2 = -480 + 480 + 106x + -106x + -2x2 + 2x2

Combine like terms: -480 + 480 = 0
480 + -106x + 2x2 = 0 + 106x + -106x + -2x2 + 2x2
480 + -106x + 2x2 = 106x + -106x + -2x2 + 2x2

Combine like terms: 106x + -106x = 0
480 + -106x + 2x2 = 0 + -2x2 + 2x2
480 + -106x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
480 + -106x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(240 + -53x + x2) = 0

Factor a trinomial.
2((5 + -1x)(48 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(48 + -1x)' equal to zero and attempt to solve:

Simplifying
48 + -1x = 0

Solving
48 + -1x = 0

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

Add '-48' to each side of the equation.
48 + -48 + -1x = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -1x = 0 + -48
-1x = 0 + -48

Combine like terms: 0 + -48 = -48
-1x = -48

Divide each side by '-1'.
x = 48

Simplifying
x = 48
Solution
x = {5, 48}