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

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

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

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

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

Reorder the terms for easier multiplication:
9 + 6y = 3y(3 + 2y)
9 + 6y = (3 * 3y + 2y * 3y)
9 + 6y = (9y + 6y2)

Solving
9 + 6y = 9y + 6y2

Solving for variable 'y'.

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

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

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Subproblem 2
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
Solution
y = {1, -1.5}