(y+5)(y-3)=0

Solution for (y+5)(y-3)=0 equation:

Simplifying
(y + 5)(y + -3) = 0

Reorder the terms:
(5 + y)(y + -3) = 0

Reorder the terms:
(5 + y)(-3 + y) = 0

Multiply (5 + y) * (-3 + y)
(5(-3 + y) + y(-3 + y)) = 0
((-3 * 5 + y * 5) + y(-3 + y)) = 0
((-15 + 5y) + y(-3 + y)) = 0
(-15 + 5y + (-3 * y + y * y)) = 0
(-15 + 5y + (-3y + y2)) = 0

Combine like terms: 5y + -3y = 2y
(-15 + 2y + y2) = 0

Solving
-15 + 2y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -1y)(3 + -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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5, 3}