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

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

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

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

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

Combine like terms: -1w + 12w = 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}