(y-9)(y+2)=0

Solution for (y-9)(y+2)=0 equation:

Simplifying
(y + -9)(y + 2) = 0

Reorder the terms:
(-9 + y)(y + 2) = 0

Reorder the terms:
(-9 + y)(2 + y) = 0

Multiply (-9 + y) * (2 + y)
(-9(2 + y) + y(2 + y)) = 0
((2 * -9 + y * -9) + y(2 + y)) = 0
((-18 + -9y) + y(2 + y)) = 0
(-18 + -9y + (2 * y + y * y)) = 0
(-18 + -9y + (2y + y2)) = 0

Combine like terms: -9y + 2y = -7y
(-18 + -7y + y2) = 0

Solving
-18 + -7y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(9 + -1y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
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 = {-2, 9}