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

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

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

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

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

Multiply (6 + 5y) * (5 + 6y)
(6(5 + 6y) + 5y * (5 + 6y)) = 0
((5 * 6 + 6y * 6) + 5y * (5 + 6y)) = 0
((30 + 36y) + 5y * (5 + 6y)) = 0
(30 + 36y + (5 * 5y + 6y * 5y)) = 0
(30 + 36y + (25y + 30y2)) = 0

Combine like terms: 36y + 25y = 61y
(30 + 61y + 30y2) = 0

Solving
30 + 61y + 30y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 6y)' equal to zero and attempt to solve:

Simplifying
5 + 6y = 0

Solving
5 + 6y = 0

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

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

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

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

Divide each side by '6'.
y = -0.8333333333

Simplifying
y = -0.8333333333
Solution
y = {-1.2, -0.8333333333}