(y-5)(y+3)=9

Solution for (y-5)(y+3)=9 equation:

Simplifying
(y + -5)(y + 3) = 9

Reorder the terms:
(-5 + y)(y + 3) = 9

Reorder the terms:
(-5 + y)(3 + y) = 9

Multiply (-5 + y) * (3 + y)
(-5(3 + y) + y(3 + y)) = 9
((3 * -5 + y * -5) + y(3 + y)) = 9
((-15 + -5y) + y(3 + y)) = 9
(-15 + -5y + (3 * y + y * y)) = 9
(-15 + -5y + (3y + y2)) = 9

Combine like terms: -5y + 3y = -2y
(-15 + -2y + y2) = 9

Solving
-15 + -2y + y2 = 9

Solving for variable 'y'.

Reorder the terms:
-15 + -9 + -2y + y2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + -2y + y2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + -2y + y2 = 0

Factor a trinomial.
(-4 + -1y)(6 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-4, 6}