(2w-9)(1-w)=0

Solution for (2w-9)(1-w)=0 equation:

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

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

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

Combine like terms: 9w + 2w = 11w
(-9 + 11w + -2w2) = 0

Solving
-9 + 11w + -2w2 = 0

Solving for variable 'w'.

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {4.5, 1}