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

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

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

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

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

Multiply (-9 + w) * (2 + w)
(-9(2 + w) + w(2 + w)) = 0
((2 * -9 + w * -9) + w(2 + w)) = 0
((-18 + -9w) + w(2 + w)) = 0
(-18 + -9w + (2 * w + w * w)) = 0
(-18 + -9w + (2w + w2)) = 0

Combine like terms: -9w + 2w = -7w
(-18 + -7w + w2) = 0

Solving
-18 + -7w + w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

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

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

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

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

Simplifying
w = -2
Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

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

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

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

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

Simplifying
w = 9
Solution
w = {-2, 9}