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

Solution for (5-w)(2w-3)=0 equation:

Simplifying
(5 + -1w)(2w + -3) = 0

Reorder the terms:
(5 + -1w)(-3 + 2w) = 0

Multiply (5 + -1w) * (-3 + 2w)
(5(-3 + 2w) + -1w * (-3 + 2w)) = 0
((-3 * 5 + 2w * 5) + -1w * (-3 + 2w)) = 0
((-15 + 10w) + -1w * (-3 + 2w)) = 0
(-15 + 10w + (-3 * -1w + 2w * -1w)) = 0
(-15 + 10w + (3w + -2w2)) = 0

Combine like terms: 10w + 3w = 13w
(-15 + 13w + -2w2) = 0

Solving
-15 + 13w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + w)(3 + -2w) = 0

Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve:

Simplifying
-5 + w = 0

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

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

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

Simplifying
w = 5
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 = {5, 1.5}