(4w+7)(6+w)=0

Solution for (4w+7)(6+w)=0 equation:

Simplifying
(4w + 7)(6 + w) = 0

Reorder the terms:
(7 + 4w)(6 + w) = 0

Multiply (7 + 4w) * (6 + w)
(7(6 + w) + 4w * (6 + w)) = 0
((6 * 7 + w * 7) + 4w * (6 + w)) = 0
((42 + 7w) + 4w * (6 + w)) = 0
(42 + 7w + (6 * 4w + w * 4w)) = 0
(42 + 7w + (24w + 4w2)) = 0

Combine like terms: 7w + 24w = 31w
(42 + 31w + 4w2) = 0

Solving
42 + 31w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(7 + 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 '(7 + 4w)' equal to zero and attempt to solve:

Simplifying
7 + 4w = 0

Solving
7 + 4w = 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 + 4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4w = 0 + -7
4w = 0 + -7

Combine like terms: 0 + -7 = -7
4w = -7

Divide each side by '4'.
w = -1.75

Simplifying
w = -1.75
Solution
w = {-6, -1.75}