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

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

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

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

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

Multiply (-3 + w) * (9 + w)
(-3(9 + w) + w(9 + w)) = 0
((9 * -3 + w * -3) + w(9 + w)) = 0
((-27 + -3w) + w(9 + w)) = 0
(-27 + -3w + (9 * w + w * w)) = 0
(-27 + -3w + (9w + w2)) = 0

Combine like terms: -3w + 9w = 6w
(-27 + 6w + w2) = 0

Solving
-27 + 6w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -1w)(3 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

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