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

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

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

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

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