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

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

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

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

Multiply (9 + w) * (6 + 4w)
(9(6 + 4w) + w(6 + 4w)) = 0
((6 * 9 + 4w * 9) + w(6 + 4w)) = 0
((54 + 36w) + w(6 + 4w)) = 0
(54 + 36w + (6 * w + 4w * w)) = 0
(54 + 36w + (6w + 4w2)) = 0

Combine like terms: 36w + 6w = 42w
(54 + 42w + 4w2) = 0

Solving
54 + 42w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 21w + 2w2) = 0

Factor a trinomial.
2((9 + w)(3 + 2w)) = 0

Ignore the factor 2.
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 '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-9, -1.5}