3y(3y+5)=6

Solution for 3y(3y+5)=6 equation:

Simplifying
3y(3y + 5) = 6

Reorder the terms:
3y(5 + 3y) = 6
(5 * 3y + 3y * 3y) = 6
(15y + 9y2) = 6

Solving
15y + 9y2 = 6

Solving for variable 'y'.

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

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

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

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

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {-2, 0.3333333333}