(3w-5)(6-w)=0

Solution for (3w-5)(6-w)=0 equation:

Simplifying
(3w + -5)(6 + -1w) = 0

Reorder the terms:
(-5 + 3w)(6 + -1w) = 0

Multiply (-5 + 3w) * (6 + -1w)
(-5(6 + -1w) + 3w * (6 + -1w)) = 0
((6 * -5 + -1w * -5) + 3w * (6 + -1w)) = 0
((-30 + 5w) + 3w * (6 + -1w)) = 0
(-30 + 5w + (6 * 3w + -1w * 3w)) = 0
(-30 + 5w + (18w + -3w2)) = 0

Combine like terms: 5w + 18w = 23w
(-30 + 23w + -3w2) = 0

Solving
-30 + 23w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + w)(5 + -3w) = 0

Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve:

Simplifying
-6 + w = 0

Solving
-6 + w = 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 + w = 0 + 6

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

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

Simplifying
w = 6
Subproblem 2
Set the factor '(5 + -3w)' equal to zero and attempt to solve:

Simplifying
5 + -3w = 0

Solving
5 + -3w = 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 + -3w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3w = 0 + -5
-3w = 0 + -5

Combine like terms: 0 + -5 = -5
-3w = -5

Divide each side by '-3'.
w = 1.666666667

Simplifying
w = 1.666666667
Solution
w = {6, 1.666666667}