(3y-2)(3+y)=0

Solution for (3y-2)(3+y)=0 equation:

Simplifying
(3y + -2)(3 + y) = 0

Reorder the terms:
(-2 + 3y)(3 + y) = 0

Multiply (-2 + 3y) * (3 + y)
(-2(3 + y) + 3y * (3 + y)) = 0
((3 * -2 + y * -2) + 3y * (3 + y)) = 0
((-6 + -2y) + 3y * (3 + y)) = 0
(-6 + -2y + (3 * 3y + y * 3y)) = 0
(-6 + -2y + (9y + 3y2)) = 0

Combine like terms: -2y + 9y = 7y
(-6 + 7y + 3y2) = 0

Solving
-6 + 7y + 3y2 = 0

Solving for variable 'y'.

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

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

Simplifying
2 + -3y = 0

Solving
2 + -3y = 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 + -3y = 0 + -2

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-3, 0.6666666667}