(5y+6)(9y+7)=0

Solution for (5y+6)(9y+7)=0 equation:

Simplifying
(5y + 6)(9y + 7) = 0

Reorder the terms:
(6 + 5y)(9y + 7) = 0

Reorder the terms:
(6 + 5y)(7 + 9y) = 0

Multiply (6 + 5y) * (7 + 9y)
(6(7 + 9y) + 5y * (7 + 9y)) = 0
((7 * 6 + 9y * 6) + 5y * (7 + 9y)) = 0
((42 + 54y) + 5y * (7 + 9y)) = 0
(42 + 54y + (7 * 5y + 9y * 5y)) = 0
(42 + 54y + (35y + 45y2)) = 0

Combine like terms: 54y + 35y = 89y
(42 + 89y + 45y2) = 0

Solving
42 + 89y + 45y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + 5y)(7 + 9y) = 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 '(7 + 9y)' equal to zero and attempt to solve:

Simplifying
7 + 9y = 0

Solving
7 + 9y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 9y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9y = 0 + -7
9y = 0 + -7

Combine like terms: 0 + -7 = -7
9y = -7

Divide each side by '9'.
y = -0.7777777778

Simplifying
y = -0.7777777778
Solution
y = {-1.2, -0.7777777778}