6y=3y^2-9

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

Simplifying
6y = 3y2 + -9

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

Solving
6y = -9 + 3y2

Solving for variable 'y'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 2y + -1y2) = 0

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

Ignore the factor 3.
Subproblem 1
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
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}