(3w-1)(4-w)=0

Solution for (3w-1)(4-w)=0 equation:

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

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

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

Combine like terms: 1w + 12w = 13w
(-4 + 13w + -3w2) = 0

Solving
-4 + 13w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + w)(1 + -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 '(1 + -3w)' equal to zero and attempt to solve:

Simplifying
1 + -3w = 0

Solving
1 + -3w = 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 + -3w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3w = 0 + -1
-3w = 0 + -1

Combine like terms: 0 + -1 = -1
-3w = -1

Divide each side by '-3'.
w = 0.3333333333

Simplifying
w = 0.3333333333
Solution
w = {4, 0.3333333333}