(2w-1)(3-w)=0

Solution for (2w-1)(3-w)=0 equation:

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

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

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

Combine like terms: 1w + 6w = 7w
(-3 + 7w + -2w2) = 0

Solving
-3 + 7w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + w)(1 + -2w) = 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 '(1 + -2w)' equal to zero and attempt to solve:

Simplifying
1 + -2w = 0

Solving
1 + -2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w = 0 + -1
-2w = 0 + -1

Combine like terms: 0 + -1 = -1
-2w = -1

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {3, 0.5}