(4w+9)(3+w)=0

Solution for (4w+9)(3+w)=0 equation:

Simplifying
(4w + 9)(3 + w) = 0

Reorder the terms:
(9 + 4w)(3 + w) = 0

Multiply (9 + 4w) * (3 + w)
(9(3 + w) + 4w * (3 + w)) = 0
((3 * 9 + w * 9) + 4w * (3 + w)) = 0
((27 + 9w) + 4w * (3 + w)) = 0
(27 + 9w + (3 * 4w + w * 4w)) = 0
(27 + 9w + (12w + 4w2)) = 0

Combine like terms: 9w + 12w = 21w
(27 + 21w + 4w2) = 0

Solving
27 + 21w + 4w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
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 = {-3, -2.25}