(4w+9)(6+w)=0

Solution for (4w+9)(6+w)=0 equation:

Simplifying
(4w + 9)(6 + w) = 0

Reorder the terms:
(9 + 4w)(6 + w) = 0

Multiply (9 + 4w) * (6 + w)
(9(6 + w) + 4w * (6 + w)) = 0
((6 * 9 + w * 9) + 4w * (6 + w)) = 0
((54 + 9w) + 4w * (6 + w)) = 0
(54 + 9w + (6 * 4w + w * 4w)) = 0
(54 + 9w + (24w + 4w2)) = 0

Combine like terms: 9w + 24w = 33w
(54 + 33w + 4w2) = 0

Solving
54 + 33w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(9 + 4w) = 0

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

Simplifying
6 + w = 0

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

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

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

Simplifying
w = -6
Subproblem 2
Set the factor '(9 + 4w)' equal to zero and attempt to solve:

Simplifying
9 + 4w = 0

Solving
9 + 4w = 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 + 4w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4w = 0 + -9
4w = 0 + -9

Combine like terms: 0 + -9 = -9
4w = -9

Divide each side by '4'.
w = -2.25

Simplifying
w = -2.25
Solution
w = {-6, -2.25}