(5w-6)(9-w)=0

Solution for (5w-6)(9-w)=0 equation:

Simplifying
(5w + -6)(9 + -1w) = 0

Reorder the terms:
(-6 + 5w)(9 + -1w) = 0

Multiply (-6 + 5w) * (9 + -1w)
(-6(9 + -1w) + 5w * (9 + -1w)) = 0
((9 * -6 + -1w * -6) + 5w * (9 + -1w)) = 0
((-54 + 6w) + 5w * (9 + -1w)) = 0
(-54 + 6w + (9 * 5w + -1w * 5w)) = 0
(-54 + 6w + (45w + -5w2)) = 0

Combine like terms: 6w + 45w = 51w
(-54 + 51w + -5w2) = 0

Solving
-54 + 51w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + w)(6 + -5w) = 0

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

Simplifying
-9 + w = 0

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

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

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

Simplifying
w = 9
Subproblem 2
Set the factor '(6 + -5w)' equal to zero and attempt to solve:

Simplifying
6 + -5w = 0

Solving
6 + -5w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5w = 0 + -6
-5w = 0 + -6

Combine like terms: 0 + -6 = -6
-5w = -6

Divide each side by '-5'.
w = 1.2

Simplifying
w = 1.2
Solution
w = {9, 1.2}