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

Solution for (1-w)(5w-9)=0 equation:

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

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

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

Combine like terms: 5w + 9w = 14w
(-9 + 14w + -5w2) = 0

Solving
-9 + 14w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + 5w)(1 + -1w) = 0

Subproblem 1
Set the factor '(-9 + 5w)' equal to zero and attempt to solve:

Simplifying
-9 + 5w = 0

Solving
-9 + 5w = 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 + 5w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5w = 0 + 9
5w = 0 + 9

Combine like terms: 0 + 9 = 9
5w = 9

Divide each side by '5'.
w = 1.8

Simplifying
w = 1.8
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 = {1.8, 1}