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

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

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

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

Multiply (3 + -1w) * (-6 + 5w)
(3(-6 + 5w) + -1w * (-6 + 5w)) = 0
((-6 * 3 + 5w * 3) + -1w * (-6 + 5w)) = 0
((-18 + 15w) + -1w * (-6 + 5w)) = 0
(-18 + 15w + (-6 * -1w + 5w * -1w)) = 0
(-18 + 15w + (6w + -5w2)) = 0

Combine like terms: 15w + 6w = 21w
(-18 + 21w + -5w2) = 0

Solving
-18 + 21w + -5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve:

Simplifying
-3 + w = 0

Solving
-3 + w = 0

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

Add '3' to each side of the equation.
-3 + 3 + w = 0 + 3

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

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

Simplifying
w = 3
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 = {3, 1.2}