(2w-3)(6-w)=0

Solution for (2w-3)(6-w)=0 equation:

Simplifying
(2w + -3)(6 + -1w) = 0

Reorder the terms:
(-3 + 2w)(6 + -1w) = 0

Multiply (-3 + 2w) * (6 + -1w)
(-3(6 + -1w) + 2w * (6 + -1w)) = 0
((6 * -3 + -1w * -3) + 2w * (6 + -1w)) = 0
((-18 + 3w) + 2w * (6 + -1w)) = 0
(-18 + 3w + (6 * 2w + -1w * 2w)) = 0
(-18 + 3w + (12w + -2w2)) = 0

Combine like terms: 3w + 12w = 15w
(-18 + 15w + -2w2) = 0

Solving
-18 + 15w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + w)(3 + -2w) = 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 '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {6, 1.5}