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

Solution for (8+w)(2w+3)=0 equation:

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

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

Multiply (8 + w) * (3 + 2w)
(8(3 + 2w) + w(3 + 2w)) = 0
((3 * 8 + 2w * 8) + w(3 + 2w)) = 0
((24 + 16w) + w(3 + 2w)) = 0
(24 + 16w + (3 * w + 2w * w)) = 0
(24 + 16w + (3w + 2w2)) = 0

Combine like terms: 16w + 3w = 19w
(24 + 19w + 2w2) = 0

Solving
24 + 19w + 2w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
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 = {-8, -1.5}