(3x+8)(2x+6)
Open the brackets
6x^2 + 18x + 16x + 48 = 0
Collect like terms
6x^2 + 34x + 48 = 0
Divide through by 2
3x^2 + 17x + 24 = 0
Solving by factorization method
3x^2 + 9x + 8x + 24 = 0
(3x^2 + 9x) + (8x + 24) = 0
3x(x + 3) + 3(x + 3) = 0
(3x + 3)(x +3) = 0
3x + 3 = 0 or x + 3 = 0
This imply that:
3x = -3 or x = -3
x = -3/3 or x = -3
Therefore:
x = -1 or x = -3