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

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

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

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

Multiply (5 + y) * (1 + 5y)
(5(1 + 5y) + y(1 + 5y)) = 0
((1 * 5 + 5y * 5) + y(1 + 5y)) = 0
((5 + 25y) + y(1 + 5y)) = 0
(5 + 25y + (1 * y + 5y * y)) = 0
(5 + 25y + (1y + 5y2)) = 0

Combine like terms: 25y + 1y = 26y
(5 + 26y + 5y2) = 0

Solving
5 + 26y + 5y2 = 0

Solving for variable 'y'.

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

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

Simplifying
5 + y = 0

Solving
5 + y = 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 + y = 0 + -5

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

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

Simplifying
y = -5
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 = {-5, -0.2}