3/(x + 4) = (x + 2)/5
Multiply both sides by 5 :
5 × 3/(x + 4) = 5 × (x + 2)/5
15/(x + 4) = x + 2
Multiply both sides by x + 4 :
(x + 4) × 15/(x + 4) = (x + 4) × (x + 2)
Provided that x + 4 ≠ 0, we can cancel the factors of x + 4 on the left side:
15 = (x + 4) (x + 2)
Expand the product on the right side:
15 = x² + 6x + 8
Move everything to one side:
0 = x² + 6x - 7
We can factorize easily in this case
0 = (x + 7) (x - 1)
Then
x + 7 = 0 or x - 1 = 0
⇒ x = -7 or x = 1