For both questions, I recommend expanding, collecting like terms and arranging in standard form. Then you may try to factor, complete the square or use the quadratic formula.
1. x(2x - 3) - 2(3 + 2x) = -4(x + 1)
My attempt:
x(2x - 3) - 2(3 + 2x) = -4(x + 1)
x(2x - 3) - 2(3 + 2x) + 4(x + 1) = 0
I am not sure where to go from there, should I expand this? I do not know what to do with all these x's and how I will figure out the roots if there are all these x's.
2. 3(x - 2)(x + 1) - 4 = 2(x - 1)^2
Same deal here....