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

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

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

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

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

Combine like terms: 8w + 3w = 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}