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

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

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

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

Multiply (3 + w) * (6 + 5w)
(3(6 + 5w) + w(6 + 5w)) = 0
((6 * 3 + 5w * 3) + w(6 + 5w)) = 0
((18 + 15w) + w(6 + 5w)) = 0
(18 + 15w + (6 * w + 5w * w)) = 0
(18 + 15w + (6w + 5w2)) = 0

Combine like terms: 15w + 6w = 21w
(18 + 21w + 5w2) = 0

Solving
18 + 21w + 5w2 = 0

Solving for variable 'w'.

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

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

Simplifying
3 + w = 0

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

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

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

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

Simplifying
6 + 5w = 0

Solving
6 + 5w = 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 + 5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5w = 0 + -6
5w = 0 + -6

Combine like terms: 0 + -6 = -6
5w = -6

Divide each side by '5'.
w = -1.2

Simplifying
w = -1.2
Solution
w = {-3, -1.2}