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

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

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

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

Multiply (8 + 3w) * (2 + w)
(8(2 + w) + 3w * (2 + w)) = 0
((2 * 8 + w * 8) + 3w * (2 + w)) = 0
((16 + 8w) + 3w * (2 + w)) = 0
(16 + 8w + (2 * 3w + w * 3w)) = 0
(16 + 8w + (6w + 3w2)) = 0

Combine like terms: 8w + 6w = 14w
(16 + 14w + 3w2) = 0

Solving
16 + 14w + 3w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(8 + 3w)' equal to zero and attempt to solve:

Simplifying
8 + 3w = 0

Solving
8 + 3w = 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 + 3w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3w = 0 + -8
3w = 0 + -8

Combine like terms: 0 + -8 = -8
3w = -8

Divide each side by '3'.
w = -2.666666667

Simplifying
w = -2.666666667
Subproblem 2
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
Solution
w = {-2.666666667, -2}