(2w-9)(5-w)=0

Solution for (2w-9)(5-w)=0 equation:

Simplifying
(2w + -9)(5 + -1w) = 0

Reorder the terms:
(-9 + 2w)(5 + -1w) = 0

Multiply (-9 + 2w) * (5 + -1w)
(-9(5 + -1w) + 2w * (5 + -1w)) = 0
((5 * -9 + -1w * -9) + 2w * (5 + -1w)) = 0
((-45 + 9w) + 2w * (5 + -1w)) = 0
(-45 + 9w + (5 * 2w + -1w * 2w)) = 0
(-45 + 9w + (10w + -2w2)) = 0

Combine like terms: 9w + 10w = 19w
(-45 + 19w + -2w2) = 0

Solving
-45 + 19w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + w)(9 + -2w) = 0

Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve:

Simplifying
-5 + w = 0

Solving
-5 + w = 0

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

Add '5' to each side of the equation.
-5 + 5 + w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + w = 0 + 5
w = 0 + 5

Combine like terms: 0 + 5 = 5
w = 5

Simplifying
w = 5
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 = {5, 4.5}