(y-5)(y+9)=15

Solution for (y-5)(y+9)=15 equation:

Simplifying
(y + -5)(y + 9) = 15

Reorder the terms:
(-5 + y)(y + 9) = 15

Reorder the terms:
(-5 + y)(9 + y) = 15

Multiply (-5 + y) * (9 + y)
(-5(9 + y) + y(9 + y)) = 15
((9 * -5 + y * -5) + y(9 + y)) = 15
((-45 + -5y) + y(9 + y)) = 15
(-45 + -5y + (9 * y + y * y)) = 15
(-45 + -5y + (9y + y2)) = 15

Combine like terms: -5y + 9y = 4y
(-45 + 4y + y2) = 15

Solving
-45 + 4y + y2 = 15

Solving for variable 'y'.

Reorder the terms:
-45 + -15 + 4y + y2 = 15 + -15

Combine like terms: -45 + -15 = -60
-60 + 4y + y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-60 + 4y + y2 = 0

Factor a trinomial.
(-10 + -1y)(6 + -1y) = 0

Subproblem 1
Set the factor '(-10 + -1y)' equal to zero and attempt to solve:

Simplifying
-10 + -1y = 0

Solving
-10 + -1y = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1y = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1y = 0 + 10
-1y = 0 + 10

Combine like terms: 0 + 10 = 10
-1y = 10

Divide each side by '-1'.
y = -10

Simplifying
y = -10
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 = {-10, 6}