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

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

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

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

Multiply (-9 + 2w) * (6 + w)
(-9(6 + w) + 2w * (6 + w)) = 0
((6 * -9 + w * -9) + 2w * (6 + w)) = 0
((-54 + -9w) + 2w * (6 + w)) = 0
(-54 + -9w + (6 * 2w + w * 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}