(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 = 13w
(3 + 13w + 4w2) = 0

Solving
3 + 13w + 4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
3 + w = 0

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

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

Combine like terms: 0 + -3 = -3
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}