2y(3y+1)=9y+3

Solution for 2y(3y+1)=9y+3 equation:

Simplifying
2y(3y + 1) = 9y + 3

Reorder the terms:
2y(1 + 3y) = 9y + 3
(1 * 2y + 3y * 2y) = 9y + 3
(2y + 6y2) = 9y + 3

Reorder the terms:
2y + 6y2 = 3 + 9y

Solving
2y + 6y2 = 3 + 9y

Solving for variable 'y'.

Reorder the terms:
-3 + 2y + -9y + 6y2 = 3 + 9y + -3 + -9y

Combine like terms: 2y + -9y = -7y
-3 + -7y + 6y2 = 3 + 9y + -3 + -9y

Reorder the terms:
-3 + -7y + 6y2 = 3 + -3 + 9y + -9y

Combine like terms: 3 + -3 = 0
-3 + -7y + 6y2 = 0 + 9y + -9y
-3 + -7y + 6y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
-3 + -7y + 6y2 = 0

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

Subproblem 1
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
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 = {-0.3333333333, 1.5}