(2w+9)(6-w)=0

Solution for (2w+9)(6-w)=0 equation:

Simplifying
(2w + 9)(6 + -1w) = 0

Reorder the terms:
(9 + 2w)(6 + -1w) = 0

Multiply (9 + 2w) * (6 + -1w)
(9(6 + -1w) + 2w * (6 + -1w)) = 0
((6 * 9 + -1w * 9) + 2w * (6 + -1w)) = 0
((54 + -9w) + 2w * (6 + -1w)) = 0
(54 + -9w + (6 * 2w + -1w * 2w)) = 0
(54 + -9w + (12w + -2w2)) = 0

Combine like terms: -9w + 12w = 3w
(54 + 3w + -2w2) = 0

Solving
54 + 3w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -1w)(9 + 2w) = 0

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

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve:

Simplifying
9 + 2w = 0

Solving
9 + 2w = 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 + 2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2w = 0 + -9
2w = 0 + -9

Combine like terms: 0 + -9 = -9
2w = -9

Divide each side by '2'.
w = -4.5

Simplifying
w = -4.5
Solution
w = {6, -4.5}