(4w+9)(2+w)=0

Solution for (4w+9)(2+w)=0 equation:

Simplifying
(4w + 9)(2 + w) = 0

Reorder the terms:
(9 + 4w)(2 + w) = 0

Multiply (9 + 4w) * (2 + w)
(9(2 + w) + 4w * (2 + w)) = 0
((2 * 9 + w * 9) + 4w * (2 + w)) = 0
((18 + 9w) + 4w * (2 + w)) = 0
(18 + 9w + (2 * 4w + w * 4w)) = 0
(18 + 9w + (8w + 4w2)) = 0

Combine like terms: 9w + 8w = 17w
(18 + 17w + 4w2) = 0

Solving
18 + 17w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + 4w)(2 + w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-2.25, -2}