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

Solution for (4-w)(2w-9)=0 equation:

Simplifying
(4 + -1w)(2w + -9) = 0

Reorder the terms:
(4 + -1w)(-9 + 2w) = 0

Multiply (4 + -1w) * (-9 + 2w)
(4(-9 + 2w) + -1w * (-9 + 2w)) = 0
((-9 * 4 + 2w * 4) + -1w * (-9 + 2w)) = 0
((-36 + 8w) + -1w * (-9 + 2w)) = 0
(-36 + 8w + (-9 * -1w + 2w * -1w)) = 0
(-36 + 8w + (9w + -2w2)) = 0

Combine like terms: 8w + 9w = 17w
(-36 + 17w + -2w2) = 0

Solving
-36 + 17w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + 2w)(4 + -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 '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {4.5, 4}