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

Solution for (3+w)(2w-9)=0 equation:

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

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

Multiply (3 + w) * (-9 + 2w)
(3(-9 + 2w) + w(-9 + 2w)) = 0
((-9 * 3 + 2w * 3) + w(-9 + 2w)) = 0
((-27 + 6w) + w(-9 + 2w)) = 0
(-27 + 6w + (-9 * w + 2w * w)) = 0
(-27 + 6w + (-9w + 2w2)) = 0

Combine like terms: 6w + -9w = -3w
(-27 + -3w + 2w2) = 0

Solving
-27 + -3w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(9 + -2w) = 0

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

Simplifying
9 + -2w = 0

Solving
9 + -2w = 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 + -2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2w = 0 + -9
-2w = 0 + -9

Combine like terms: 0 + -9 = -9
-2w = -9

Divide each side by '-2'.
w = 4.5

Simplifying
w = 4.5
Solution
w = {-3, 4.5}