-4(y-9)(-y-6)=0

Solution for -4(y-9)(-y-6)=0 equation:

Simplifying
-4(y + -9)(-1y + -6) = 0

Reorder the terms:
-4(-9 + y)(-1y + -6) = 0

Reorder the terms:
-4(-9 + y)(-6 + -1y) = 0

Multiply (-9 + y) * (-6 + -1y)
-4(-9(-6 + -1y) + y(-6 + -1y)) = 0
-4((-6 * -9 + -1y * -9) + y(-6 + -1y)) = 0
-4((54 + 9y) + y(-6 + -1y)) = 0
-4(54 + 9y + (-6 * y + -1y * y)) = 0
-4(54 + 9y + (-6y + -1y2)) = 0

Combine like terms: 9y + -6y = 3y
-4(54 + 3y + -1y2) = 0
(54 * -4 + 3y * -4 + -1y2 * -4) = 0
(-216 + -12y + 4y2) = 0

Solving
-216 + -12y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-54 + -3y + y2) = 0

Factor a trinomial.
4((-6 + -1y)(9 + -1y)) = 0

Ignore the factor 4.
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 '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-6, 9}