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

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

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

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

Multiply (3 + w) * (4 + 3w)
(3(4 + 3w) + w(4 + 3w)) = 0
((4 * 3 + 3w * 3) + w(4 + 3w)) = 0
((12 + 9w) + w(4 + 3w)) = 0
(12 + 9w + (4 * w + 3w * w)) = 0
(12 + 9w + (4w + 3w2)) = 0

Combine like terms: 9w + 4w = 13w
(12 + 13w + 3w2) = 0

Solving
12 + 13w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(4 + 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 '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w = 0 + -4
3w = 0 + -4

Combine like terms: 0 + -4 = -4
3w = -4

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
Solution
w = {-3, -1.333333333}