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

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

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

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

Multiply (6 + w) * (9 + 4w)
(6(9 + 4w) + w(9 + 4w)) = 0
((9 * 6 + 4w * 6) + w(9 + 4w)) = 0
((54 + 24w) + w(9 + 4w)) = 0
(54 + 24w + (9 * w + 4w * w)) = 0
(54 + 24w + (9w + 4w2)) = 0

Combine like terms: 24w + 9w = 33w
(54 + 33w + 4w2) = 0

Solving
54 + 33w + 4w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
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 = {-6, -2.25}