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

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

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

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

Multiply (9 + w) * (1 + 4w)
(9(1 + 4w) + w(1 + 4w)) = 0
((1 * 9 + 4w * 9) + w(1 + 4w)) = 0
((9 + 36w) + w(1 + 4w)) = 0
(9 + 36w + (1 * w + 4w * w)) = 0
(9 + 36w + (1w + 4w2)) = 0

Combine like terms: 36w + 1w = 37w
(9 + 37w + 4w2) = 0

Solving
9 + 37w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + w)(1 + 4w) = 0

Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

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

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

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

Simplifying
w = -9
Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve:

Simplifying
1 + 4w = 0

Solving
1 + 4w = 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 + 4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4w = 0 + -1
4w = 0 + -1

Combine like terms: 0 + -1 = -1
4w = -1

Divide each side by '4'.
w = -0.25

Simplifying
w = -0.25
Solution
w = {-9, -0.25}