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

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

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

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

Multiply (6 + 4w) * (7 + w)
(6(7 + w) + 4w * (7 + w)) = 0
((7 * 6 + w * 6) + 4w * (7 + w)) = 0
((42 + 6w) + 4w * (7 + w)) = 0
(42 + 6w + (7 * 4w + w * 4w)) = 0
(42 + 6w + (28w + 4w2)) = 0

Combine like terms: 6w + 28w = 34w
(42 + 34w + 4w2) = 0

Solving
42 + 34w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 17w + 2w2) = 0

Factor a trinomial.
2((7 + w)(3 + 2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

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

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

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

Simplifying
w = -7
Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

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

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

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

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-7, -1.5}