-9=3y(y+4)

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

Simplifying
-9 = 3y(y + 4)

Reorder the terms:
-9 = 3y(4 + y)
-9 = (4 * 3y + y * 3y)
-9 = (12y + 3y2)

Solving
-9 = 12y + 3y2

Solving for variable 'y'.

Reorder the terms:
-9 + -12y + -3y2 = 12y + -12y + 3y2 + -3y2

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

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

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

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

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

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

Simplifying
y = -3
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-3, -1}