0=-4y^2+36y-72

Solution for 0=-4y^2+36y-72 equation:

Simplifying
0 = -4y2 + 36y + -72

Reorder the terms:
0 = -72 + 36y + -4y2

Solving
0 = -72 + 36y + -4y2

Solving for variable 'y'.

Combine like terms: 0 + 72 = 72
72 + -36y + 4y2 = -72 + 36y + -4y2 + 72 + -36y + 4y2

Reorder the terms:
72 + -36y + 4y2 = -72 + 72 + 36y + -36y + -4y2 + 4y2

Combine like terms: -72 + 72 = 0
72 + -36y + 4y2 = 0 + 36y + -36y + -4y2 + 4y2
72 + -36y + 4y2 = 36y + -36y + -4y2 + 4y2

Combine like terms: 36y + -36y = 0
72 + -36y + 4y2 = 0 + -4y2 + 4y2
72 + -36y + 4y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
72 + -36y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9y + y2) = 0

Factor a trinomial.
4((3 + -1y)(6 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

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

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

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

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

Simplifying
y = 3
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 = {3, 6}