(5y+1)(6+y)=0

Solution for (5y+1)(6+y)=0 equation:

Simplifying
(5y + 1)(6 + y) = 0

Reorder the terms:
(1 + 5y)(6 + y) = 0

Multiply (1 + 5y) * (6 + y)
(1(6 + y) + 5y * (6 + y)) = 0
((6 * 1 + y * 1) + 5y * (6 + y)) = 0
((6 + 1y) + 5y * (6 + y)) = 0
(6 + 1y + (6 * 5y + y * 5y)) = 0
(6 + 1y + (30y + 5y2)) = 0

Combine like terms: 1y + 30y = 31y
(6 + 31y + 5y2) = 0

Solving
6 + 31y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + y)(1 + 5y) = 0

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

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

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

Simplifying
1 + 5y = 0

Solving
1 + 5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {-6, -0.2}