(6+w)(3w+7)=0

Solution for (6+w)(3w+7)=0 equation:

Simplifying
(6 + w)(3w + 7) = 0

Reorder the terms:
(6 + w)(7 + 3w) = 0

Multiply (6 + w) * (7 + 3w)
(6(7 + 3w) + w(7 + 3w)) = 0
((7 * 6 + 3w * 6) + w(7 + 3w)) = 0
((42 + 18w) + w(7 + 3w)) = 0
(42 + 18w + (7 * w + 3w * w)) = 0
(42 + 18w + (7w + 3w2)) = 0

Combine like terms: 18w + 7w = 25w
(42 + 25w + 3w2) = 0

Solving
42 + 25w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(7 + 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 '(7 + 3w)' equal to zero and attempt to solve:

Simplifying
7 + 3w = 0

Solving
7 + 3w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3w = 0 + -7
3w = 0 + -7

Combine like terms: 0 + -7 = -7
3w = -7

Divide each side by '3'.
w = -2.333333333

Simplifying
w = -2.333333333
Solution
w = {-6, -2.333333333}