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

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

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

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

Multiply (3 + 2w) * (2 + w)
(3(2 + w) + 2w * (2 + w)) = 0
((2 * 3 + w * 3) + 2w * (2 + w)) = 0
((6 + 3w) + 2w * (2 + w)) = 0
(6 + 3w + (2 * 2w + w * 2w)) = 0
(6 + 3w + (4w + 2w2)) = 0

Combine like terms: 3w + 4w = 7w
(6 + 7w + 2w2) = 0

Solving
6 + 7w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + w)(3 + 2w) = 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 '(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 = {-2, -1.5}