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

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

Simplifying
(3 + -1w)(2w + -9) = 0

Reorder the terms:
(3 + -1w)(-9 + 2w) = 0

Multiply (3 + -1w) * (-9 + 2w)
(3(-9 + 2w) + -1w * (-9 + 2w)) = 0
((-9 * 3 + 2w * 3) + -1w * (-9 + 2w)) = 0
((-27 + 6w) + -1w * (-9 + 2w)) = 0
(-27 + 6w + (-9 * -1w + 2w * -1w)) = 0
(-27 + 6w + (9w + -2w2)) = 0

Combine like terms: 6w + 9w = 15w
(-27 + 15w + -2w2) = 0

Solving
-27 + 15w + -2w2 = 0

Solving for variable 'w'.

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

Subproblem 1
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
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 = {4.5, 3}