(3w+1)(9+w)=0

Solution for (3w+1)(9+w)=0 equation:

Simplifying
(3w + 1)(9 + w) = 0

Reorder the terms:
(1 + 3w)(9 + w) = 0

Multiply (1 + 3w) * (9 + w)
(1(9 + w) + 3w * (9 + w)) = 0
((9 * 1 + w * 1) + 3w * (9 + w)) = 0
((9 + 1w) + 3w * (9 + w)) = 0
(9 + 1w + (9 * 3w + w * 3w)) = 0
(9 + 1w + (27w + 3w2)) = 0

Combine like terms: 1w + 27w = 28w
(9 + 28w + 3w2) = 0

Solving
9 + 28w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + w)(1 + 3w) = 0

Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

Add '-9' to each side of the equation.
9 + -9 + w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + w = 0 + -9
w = 0 + -9

Combine like terms: 0 + -9 = -9
w = -9

Simplifying
w = -9
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 = {-9, -0.3333333333}