(3y-9)(y+4)=

Solution for (3y-9)(y+4)= equation:

Simplifying
(3y + -9)(y + 4) = 0

Reorder the terms:
(-9 + 3y)(y + 4) = 0

Reorder the terms:
(-9 + 3y)(4 + y) = 0

Multiply (-9 + 3y) * (4 + y)
(-9(4 + y) + 3y * (4 + y)) = 0
((4 * -9 + y * -9) + 3y * (4 + y)) = 0
((-36 + -9y) + 3y * (4 + y)) = 0
(-36 + -9y + (4 * 3y + y * 3y)) = 0
(-36 + -9y + (12y + 3y2)) = 0

Combine like terms: -9y + 12y = 3y
(-36 + 3y + 3y2) = 0

Solving
-36 + 3y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + y + y2) = 0

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

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

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
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
Solution
y = {-4, 3}