-3y+9=-3y(2y+6)

Solution for -3y+9=-3y(2y+6) equation:

Simplifying
-3y + 9 = -3y(2y + 6)

Reorder the terms:
9 + -3y = -3y(2y + 6)

Reorder the terms:
9 + -3y = -3y(6 + 2y)
9 + -3y = (6 * -3y + 2y * -3y)
9 + -3y = (-18y + -6y2)

Solving
9 + -3y = -18y + -6y2

Solving for variable 'y'.

Combine like terms: -3y + 18y = 15y
9 + 15y + 6y2 = -18y + -6y2 + 18y + 6y2

Reorder the terms:
9 + 15y + 6y2 = -18y + 18y + -6y2 + 6y2

Combine like terms: -18y + 18y = 0
9 + 15y + 6y2 = 0 + -6y2 + 6y2
9 + 15y + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
9 + 15y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 5y + 2y2) = 0

Factor a trinomial.
3((3 + 2y)(1 + y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
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 = {-1.5, -1}