2y^2=3(y+3)

Solution for 2y^2=3(y+3) equation:

Simplifying
2y2 = 3(y + 3)

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

Solving
2y2 = 9 + 3y

Solving for variable 'y'.

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

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

Combine like terms: 9 + -9 = 0
-9 + -3y + 2y2 = 0 + 3y + -3y
-9 + -3y + 2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-9 + -3y + 2y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-1.5, 3}