(y-9)(y+3)=0

Solution for (y-9)(y+3)=0 equation:

Simplifying
(y + -9)(y + 3) = 0

Reorder the terms:
(-9 + y)(y + 3) = 0

Reorder the terms:
(-9 + y)(3 + y) = 0

Multiply (-9 + y) * (3 + y)
(-9(3 + y) + y(3 + y)) = 0
((3 * -9 + y * -9) + y(3 + y)) = 0
((-27 + -9y) + y(3 + y)) = 0
(-27 + -9y + (3 * y + y * y)) = 0
(-27 + -9y + (3y + y2)) = 0

Combine like terms: -9y + 3y = -6y
(-27 + -6y + y2) = 0

Solving
-27 + -6y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(9 + -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 '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-3, 9}