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

Solution for (2+w)(3w+1)=0 equation:

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

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

Multiply (2 + w) * (1 + 3w)
(2(1 + 3w) + w(1 + 3w)) = 0
((1 * 2 + 3w * 2) + w(1 + 3w)) = 0
((2 + 6w) + w(1 + 3w)) = 0
(2 + 6w + (1 * w + 3w * w)) = 0
(2 + 6w + (1w + 3w2)) = 0

Combine like terms: 6w + 1w = 7w
(2 + 7w + 3w2) = 0

Solving
2 + 7w + 3w2 = 0

Solving for variable 'w'.

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

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

Simplifying
2 + w = 0

Solving
2 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
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 = {-2, -0.3333333333}