(3w+5)(6+w)=0

Solution for (3w+5)(6+w)=0 equation:

Simplifying
(3w + 5)(6 + w) = 0

Reorder the terms:
(5 + 3w)(6 + w) = 0

Multiply (5 + 3w) * (6 + w)
(5(6 + w) + 3w * (6 + w)) = 0
((6 * 5 + w * 5) + 3w * (6 + w)) = 0
((30 + 5w) + 3w * (6 + w)) = 0
(30 + 5w + (6 * 3w + w * 3w)) = 0
(30 + 5w + (18w + 3w2)) = 0

Combine like terms: 5w + 18w = 23w
(30 + 23w + 3w2) = 0

Solving
30 + 23w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(5 + 3w) = 0

Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(5 + 3w)' equal to zero and attempt to solve:

Simplifying
5 + 3w = 0

Solving
5 + 3w = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3w = 0 + -5
3w = 0 + -5

Combine like terms: 0 + -5 = -5
3w = -5

Divide each side by '3'.
w = -1.666666667

Simplifying
w = -1.666666667
Solution
w = {-6, -1.666666667}