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

Solution for (1+w)(4w+9)=0 equation:

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

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

Multiply (1 + w) * (9 + 4w)
(1(9 + 4w) + w(9 + 4w)) = 0
((9 * 1 + 4w * 1) + w(9 + 4w)) = 0
((9 + 4w) + w(9 + 4w)) = 0
(9 + 4w + (9 * w + 4w * w)) = 0
(9 + 4w + (9w + 4w2)) = 0

Combine like terms: 4w + 9w = 13w
(9 + 13w + 4w2) = 0

Solving
9 + 13w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + 4w)(1 + 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 '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

Add '-1' to each side of the equation.
1 + -1 + w = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {-2.25, -1}