(w-4)(w+9)=0

Solution for (w-4)(w+9)=0 equation:

Simplifying
(w + -4)(w + 9) = 0

Reorder the terms:
(-4 + w)(w + 9) = 0

Reorder the terms:
(-4 + w)(9 + w) = 0

Multiply (-4 + w) * (9 + w)
(-4(9 + w) + w(9 + w)) = 0
((9 * -4 + w * -4) + w(9 + w)) = 0
((-36 + -4w) + w(9 + w)) = 0
(-36 + -4w + (9 * w + w * w)) = 0
(-36 + -4w + (9w + w2)) = 0

Combine like terms: -4w + 9w = 5w
(-36 + 5w + w2) = 0

Solving
-36 + 5w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -1w)(4 + -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 '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-9, 4}