Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions
x = i is a solution, and all the coefficients are real, so x = -i must also be a solution:2x^3+3x^2+2x+3 = 0(x+i)(x-i)(Ax+B) = 0 (we argued above that this must be the case)(x^2+1)(Ax+B) = 0(x^2+1)(2x+3) = 0 (we identify A and B by comparing to the first line)Therefore x = -3/2 is the third solution, and we have all the solutions
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