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

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

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

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

Multiply (3 + w) * (1 + 3w)
(3(1 + 3w) + w(1 + 3w)) = 0
((1 * 3 + 3w * 3) + w(1 + 3w)) = 0
((3 + 9w) + w(1 + 3w)) = 0
(3 + 9w + (1 * w + 3w * w)) = 0
(3 + 9w + (1w + 3w2)) = 0

Combine like terms: 9w + 1w = 10w
(3 + 10w + 3w2) = 0

Solving
3 + 10w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(1 + 3w) = 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 + 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 = {-3, -0.3333333333}