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

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

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

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

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

Combine like terms: 12w + -1w = 11w
(3 + 11w + -4w2) = 0

Solving
3 + 11w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + -1w)(1 + 4w) = 0

Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

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

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

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

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve:

Simplifying
1 + 4w = 0

Solving
1 + 4w = 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 + 4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4w = 0 + -1
4w = 0 + -1

Combine like terms: 0 + -1 = -1
4w = -1

Divide each side by '4'.
w = -0.25

Simplifying
w = -0.25
Solution
w = {3, -0.25}