0=-20x^2+320x-780

Solution for 0=-20x^2+320x-780 equation:

Simplifying
0 = -20x2 + 320x + -780

Reorder the terms:
0 = -780 + 320x + -20x2

Solving
0 = -780 + 320x + -20x2

Solving for variable 'x'.

Combine like terms: 0 + 780 = 780
780 + -320x + 20x2 = -780 + 320x + -20x2 + 780 + -320x + 20x2

Reorder the terms:
780 + -320x + 20x2 = -780 + 780 + 320x + -320x + -20x2 + 20x2

Combine like terms: -780 + 780 = 0
780 + -320x + 20x2 = 0 + 320x + -320x + -20x2 + 20x2
780 + -320x + 20x2 = 320x + -320x + -20x2 + 20x2

Combine like terms: 320x + -320x = 0
780 + -320x + 20x2 = 0 + -20x2 + 20x2
780 + -320x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
780 + -320x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(39 + -16x + x2) = 0

Factor a trinomial.
20((3 + -1x)(13 + -1x)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {3, 13}