(2w+3)(4+w)=0

Solution for (2w+3)(4+w)=0 equation:

Simplifying
(2w + 3)(4 + w) = 0

Reorder the terms:
(3 + 2w)(4 + w) = 0

Multiply (3 + 2w) * (4 + w)
(3(4 + w) + 2w * (4 + w)) = 0
((4 * 3 + w * 3) + 2w * (4 + w)) = 0
((12 + 3w) + 2w * (4 + w)) = 0
(12 + 3w + (4 * 2w + w * 2w)) = 0
(12 + 3w + (8w + 2w2)) = 0

Combine like terms: 3w + 8w = 11w
(12 + 11w + 2w2) = 0

Solving
12 + 11w + 2w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 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 + w = 0 + -4

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

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

Simplifying
w = -4
Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-4, -1.5}