(w-9)(w+16)=0

Solution for (w-9)(w+16)=0 equation:

Simplifying
(w + -9)(w + 16) = 0

Reorder the terms:
(-9 + w)(w + 16) = 0

Reorder the terms:
(-9 + w)(16 + w) = 0

Multiply (-9 + w) * (16 + w)
(-9(16 + w) + w(16 + w)) = 0
((16 * -9 + w * -9) + w(16 + w)) = 0
((-144 + -9w) + w(16 + w)) = 0
(-144 + -9w + (16 * w + w * w)) = 0
(-144 + -9w + (16w + w2)) = 0

Combine like terms: -9w + 16w = 7w
(-144 + 7w + w2) = 0

Solving
-144 + 7w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-16 + -1w)(9 + -1w) = 0

Subproblem 1
Set the factor '(-16 + -1w)' equal to zero and attempt to solve:

Simplifying
-16 + -1w = 0

Solving
-16 + -1w = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1w = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1w = 0 + 16
-1w = 0 + 16

Combine like terms: 0 + 16 = 16
-1w = 16

Divide each side by '-1'.
w = -16

Simplifying
w = -16
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 = {-16, 9}