-9y=3y^2+6

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

Simplifying
-9y = 3y2 + 6

Reorder the terms:
-9y = 6 + 3y2

Solving
-9y = 6 + 3y2

Solving for variable 'y'.

Reorder the terms:
-6 + -9y + -3y2 = 6 + 3y2 + -6 + -3y2

Reorder the terms:
-6 + -9y + -3y2 = 6 + -6 + 3y2 + -3y2

Combine like terms: 6 + -6 = 0
-6 + -9y + -3y2 = 0 + 3y2 + -3y2
-6 + -9y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-6 + -9y + -3y2 = 0

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

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

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

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

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

Simplifying
y = -2
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 = {-2, -1}