0=-2y^2+24y-72

Solution for 0=-2y^2+24y-72 equation:

Simplifying
0 = -2y2 + 24y + -72

Reorder the terms:
0 = -72 + 24y + -2y2

Solving
0 = -72 + 24y + -2y2

Solving for variable 'y'.

Combine like terms: 0 + 72 = 72
72 + -24y + 2y2 = -72 + 24y + -2y2 + 72 + -24y + 2y2

Reorder the terms:
72 + -24y + 2y2 = -72 + 72 + 24y + -24y + -2y2 + 2y2

Combine like terms: -72 + 72 = 0
72 + -24y + 2y2 = 0 + 24y + -24y + -2y2 + 2y2
72 + -24y + 2y2 = 24y + -24y + -2y2 + 2y2

Combine like terms: 24y + -24y = 0
72 + -24y + 2y2 = 0 + -2y2 + 2y2
72 + -24y + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
72 + -24y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12y + y2) = 0

Factor a trinomial.
2((6 + -1y)(6 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {6, 6}