0=-2x^2+40x-72

Solution for 0=-2x^2+40x-72 equation:

Simplifying
0 = -2x2 + 40x + -72

Reorder the terms:
0 = -72 + 40x + -2x2

Solving
0 = -72 + 40x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 72 = 72
72 + -40x + 2x2 = -72 + 40x + -2x2 + 72 + -40x + 2x2

Reorder the terms:
72 + -40x + 2x2 = -72 + 72 + 40x + -40x + -2x2 + 2x2

Combine like terms: -72 + 72 = 0
72 + -40x + 2x2 = 0 + 40x + -40x + -2x2 + 2x2
72 + -40x + 2x2 = 40x + -40x + -2x2 + 2x2

Combine like terms: 40x + -40x = 0
72 + -40x + 2x2 = 0 + -2x2 + 2x2
72 + -40x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
72 + -40x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -20x + x2) = 0

Factor a trinomial.
2((2 + -1x)(18 + -1x)) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {2, 18}