(8+w)(3w+1)=0

Solution for (8+w)(3w+1)=0 equation:

Simplifying
(8 + w)(3w + 1) = 0

Reorder the terms:
(8 + w)(1 + 3w) = 0

Multiply (8 + w) * (1 + 3w)
(8(1 + 3w) + w(1 + 3w)) = 0
((1 * 8 + 3w * 8) + w(1 + 3w)) = 0
((8 + 24w) + w(1 + 3w)) = 0
(8 + 24w + (1 * w + 3w * w)) = 0
(8 + 24w + (1w + 3w2)) = 0

Combine like terms: 24w + 1w = 25w
(8 + 25w + 3w2) = 0

Solving
8 + 25w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + w)(1 + 3w) = 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 '(1 + 3w)' equal to zero and attempt to solve:

Simplifying
1 + 3w = 0

Solving
1 + 3w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3w = 0 + -1
3w = 0 + -1

Combine like terms: 0 + -1 = -1
3w = -1

Divide each side by '3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
Solution
w = {-8, -0.3333333333}