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

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

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

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

Multiply (9 + w) * (-3 + 2w)
(9(-3 + 2w) + w(-3 + 2w)) = 0
((-3 * 9 + 2w * 9) + w(-3 + 2w)) = 0
((-27 + 18w) + w(-3 + 2w)) = 0
(-27 + 18w + (-3 * w + 2w * w)) = 0
(-27 + 18w + (-3w + 2w2)) = 0

Combine like terms: 18w + -3w = 15w
(-27 + 15w + 2w2) = 0

Solving
-27 + 15w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -1w)(3 + -2w) = 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 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

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

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-9, 1.5}