(3w+4)(6+w)=0

Solution for (3w+4)(6+w)=0 equation:

Simplifying
(3w + 4)(6 + w) = 0

Reorder the terms:
(4 + 3w)(6 + w) = 0

Multiply (4 + 3w) * (6 + w)
(4(6 + w) + 3w * (6 + w)) = 0
((6 * 4 + w * 4) + 3w * (6 + w)) = 0
((24 + 4w) + 3w * (6 + w)) = 0
(24 + 4w + (6 * 3w + w * 3w)) = 0
(24 + 4w + (18w + 3w2)) = 0

Combine like terms: 4w + 18w = 22w
(24 + 22w + 3w2) = 0

Solving
24 + 22w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(4 + 3w) = 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 '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w = 0 + -4
3w = 0 + -4

Combine like terms: 0 + -4 = -4
3w = -4

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
Solution
w = {-6, -1.333333333}