(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.
(-3 + -1y)(5 + -1y) = 0

Subproblem 1
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
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 = {-3, 5}