(8y+13)(5y+6)=0

Solution for (8y+13)(5y+6)=0 equation:

Simplifying
(8y + 13)(5y + 6) = 0

Reorder the terms:
(13 + 8y)(5y + 6) = 0

Reorder the terms:
(13 + 8y)(6 + 5y) = 0

Multiply (13 + 8y) * (6 + 5y)
(13(6 + 5y) + 8y * (6 + 5y)) = 0
((6 * 13 + 5y * 13) + 8y * (6 + 5y)) = 0
((78 + 65y) + 8y * (6 + 5y)) = 0
(78 + 65y + (6 * 8y + 5y * 8y)) = 0
(78 + 65y + (48y + 40y2)) = 0

Combine like terms: 65y + 48y = 113y
(78 + 113y + 40y2) = 0

Solving
78 + 113y + 40y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(13 + 8y)(6 + 5y) = 0

Subproblem 1
Set the factor '(13 + 8y)' equal to zero and attempt to solve:

Simplifying
13 + 8y = 0

Solving
13 + 8y = 0

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

Add '-13' to each side of the equation.
13 + -13 + 8y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 8y = 0 + -13
8y = 0 + -13

Combine like terms: 0 + -13 = -13
8y = -13

Divide each side by '8'.
y = -1.625

Simplifying
y = -1.625
Subproblem 2
Set the factor '(6 + 5y)' equal to zero and attempt to solve:

Simplifying
6 + 5y = 0

Solving
6 + 5y = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5y = 0 + -6
5y = 0 + -6

Combine like terms: 0 + -6 = -6
5y = -6

Divide each side by '5'.
y = -1.2

Simplifying
y = -1.2
Solution
y = {-1.625, -1.2}