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

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

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

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

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

Combine like terms: -1w + 27w = 26w
(9 + 26w + -3w2) = 0

Solving
9 + 26w + -3w2 = 0

Solving for variable 'w'.

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

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

Simplifying
9 + -1w = 0

Solving
9 + -1w = 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 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
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}