(3w-5)(4-w)=0

Solution for (3w-5)(4-w)=0 equation:

Simplifying
(3w + -5)(4 + -1w) = 0

Reorder the terms:
(-5 + 3w)(4 + -1w) = 0

Multiply (-5 + 3w) * (4 + -1w)
(-5(4 + -1w) + 3w * (4 + -1w)) = 0
((4 * -5 + -1w * -5) + 3w * (4 + -1w)) = 0
((-20 + 5w) + 3w * (4 + -1w)) = 0
(-20 + 5w + (4 * 3w + -1w * 3w)) = 0
(-20 + 5w + (12w + -3w2)) = 0

Combine like terms: 5w + 12w = 17w
(-20 + 17w + -3w2) = 0

Solving
-20 + 17w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + w)(5 + -3w) = 0

Subproblem 1
Set the factor '(-4 + w)' equal to zero and attempt to solve:

Simplifying
-4 + w = 0

Solving
-4 + w = 0

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

Add '4' to each side of the equation.
-4 + 4 + w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + w = 0 + 4
w = 0 + 4

Combine like terms: 0 + 4 = 4
w = 4

Simplifying
w = 4
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 = {4, 1.666666667}