(6+w)(3w+2)=0

Solution for (6+w)(3w+2)=0 equation:

Simplifying
(6 + w)(3w + 2) = 0

Reorder the terms:
(6 + w)(2 + 3w) = 0

Multiply (6 + w) * (2 + 3w)
(6(2 + 3w) + w(2 + 3w)) = 0
((2 * 6 + 3w * 6) + w(2 + 3w)) = 0
((12 + 18w) + w(2 + 3w)) = 0
(12 + 18w + (2 * w + 3w * w)) = 0
(12 + 18w + (2w + 3w2)) = 0

Combine like terms: 18w + 2w = 20w
(12 + 20w + 3w2) = 0

Solving
12 + 20w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(2 + 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 '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3w = 0 + -2

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

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

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {-6, -0.6666666667}