(3y-1)(3+y)=0

Solution for (3y-1)(3+y)=0 equation:

Simplifying
(3y + -1)(3 + y) = 0

Reorder the terms:
(-1 + 3y)(3 + y) = 0

Multiply (-1 + 3y) * (3 + y)
(-1(3 + y) + 3y * (3 + y)) = 0
((3 * -1 + y * -1) + 3y * (3 + y)) = 0
((-3 + -1y) + 3y * (3 + y)) = 0
(-3 + -1y + (3 * 3y + y * 3y)) = 0
(-3 + -1y + (9y + 3y2)) = 0

Combine like terms: -1y + 9y = 8y
(-3 + 8y + 3y2) = 0

Solving
-3 + 8y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(1 + -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 '(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 = {-3, 0.3333333333}