2y(y+2)=3(y+2)

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

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

Reorder the terms:
2y(2 + y) = 3(y + 2)
(2 * 2y + y * 2y) = 3(y + 2)
(4y + 2y2) = 3(y + 2)

Reorder the terms:
4y + 2y2 = 3(2 + y)
4y + 2y2 = (2 * 3 + y * 3)
4y + 2y2 = (6 + 3y)

Solving
4y + 2y2 = 6 + 3y

Solving for variable 'y'.

Reorder the terms:
-6 + 4y + -3y + 2y2 = 6 + 3y + -6 + -3y

Combine like terms: 4y + -3y = 1y
-6 + 1y + 2y2 = 6 + 3y + -6 + -3y

Reorder the terms:
-6 + 1y + 2y2 = 6 + -6 + 3y + -3y

Combine like terms: 6 + -6 = 0
-6 + 1y + 2y2 = 0 + 3y + -3y
-6 + 1y + 2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-6 + 1y + 2y2 = 0

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

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 '(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 = {-2, 1.5}