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

Solution for (9+y)(3y+1)=0 equation:

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

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

Multiply (9 + y) * (1 + 3y)
(9(1 + 3y) + y(1 + 3y)) = 0
((1 * 9 + 3y * 9) + y(1 + 3y)) = 0
((9 + 27y) + y(1 + 3y)) = 0
(9 + 27y + (1 * y + 3y * y)) = 0
(9 + 27y + (1y + 3y2)) = 0

Combine like terms: 27y + 1y = 28y
(9 + 28y + 3y2) = 0

Solving
9 + 28y + 3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
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 = {-9, -0.3333333333}