(2y+6)(5y+3)=0

Solution for (2y+6)(5y+3)=0 equation:

Simplifying
(2y + 6)(5y + 3) = 0

Reorder the terms:
(6 + 2y)(5y + 3) = 0

Reorder the terms:
(6 + 2y)(3 + 5y) = 0

Multiply (6 + 2y) * (3 + 5y)
(6(3 + 5y) + 2y * (3 + 5y)) = 0
((3 * 6 + 5y * 6) + 2y * (3 + 5y)) = 0
((18 + 30y) + 2y * (3 + 5y)) = 0
(18 + 30y + (3 * 2y + 5y * 2y)) = 0
(18 + 30y + (6y + 10y2)) = 0

Combine like terms: 30y + 6y = 36y
(18 + 36y + 10y2) = 0

Solving
18 + 36y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 18y + 5y2) = 0

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

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
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 = {-3, -0.6}