-4(y-3)(-y+6)=0

Solution for -4(y-3)(-y+6)=0 equation:

Simplifying
-4(y + -3)(-1y + 6) = 0

Reorder the terms:
-4(-3 + y)(-1y + 6) = 0

Reorder the terms:
-4(-3 + y)(6 + -1y) = 0

Multiply (-3 + y) * (6 + -1y)
-4(-3(6 + -1y) + y(6 + -1y)) = 0
-4((6 * -3 + -1y * -3) + y(6 + -1y)) = 0
-4((-18 + 3y) + y(6 + -1y)) = 0
-4(-18 + 3y + (6 * y + -1y * y)) = 0
-4(-18 + 3y + (6y + -1y2)) = 0

Combine like terms: 3y + 6y = 9y
-4(-18 + 9y + -1y2) = 0
(-18 * -4 + 9y * -4 + -1y2 * -4) = 0
(72 + -36y + 4y2) = 0

Solving
72 + -36y + 4y2 = 0

Solving for variable 'y'.

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}