Solve the following quadratic equation by factorization method: (2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/((x - 3)(2x + 3)) = 0

2x/(x-3) + 1/(2x+3) + (3x+9)/((x-3)(2x+3)) = 0 2x(2x+3) + (x-3) + (3x+9) = 0 4x^2 + 6x + x - 3 + 3x + 9 = 0 4x^2 + 10x + 6 = 0 2x^2 + 5x + 3 = 0 2x^2 + 2x + 3x + 3 = 0 2x(x+1) + 3(x+1) = 0 (2x+3)(x+1) = 0 Hence, x = -1, -3/2 Since, it is given that x ≠ -3/2 Hence, x = -1 is the only possible solution.