(5y+3)(2+y)=0

Solution for (5y+3)(2+y)=0 equation:

Simplifying
(5y + 3)(2 + y) = 0

Reorder the terms:
(3 + 5y)(2 + y) = 0

Multiply (3 + 5y) * (2 + y)
(3(2 + y) + 5y * (2 + y)) = 0
((2 * 3 + y * 3) + 5y * (2 + y)) = 0
((6 + 3y) + 5y * (2 + y)) = 0
(6 + 3y + (2 * 5y + y * 5y)) = 0
(6 + 3y + (10y + 5y2)) = 0

Combine like terms: 3y + 10y = 13y
(6 + 13y + 5y2) = 0

Solving
6 + 13y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + y)(3 + 5y) = 0

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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 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 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {-2, -0.6}