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

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

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

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

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

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

Combine like terms: -1y + 5y = 4y
-5(5 + 4y + -1y2) = 0
(5 * -5 + 4y * -5 + -1y2 * -5) = 0
(-25 + -20y + 5y2) = 0

Solving
-25 + -20y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -4y + y2) = 0

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

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

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

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

Divide each side by '-1'.
y = -1

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

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

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

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-1, 5}