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

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

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

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

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

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

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

Solving
-5 + 4y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-5, 1}