Final answer:
The solution to the inequality -2x²+2x+1>-3x²+3x+7 is the interval (-2, 3), obtained by simplifying and factoring the inequality.
Step-by-step explanation:
To solve the inequality -2x²+2x+1>-3x²+3x+7, we first need to simplify it into a standard form. By adding 3x² to both sides and subtracting 3x and 7, we obtain x² - x - 6 < 0. Factoring the left-hand side gives us (x-3)(x+2) < 0. To determine where this product is negative, we examine the intervals determined by the roots x = 3 and x = -2. The inequality holds when x is between -2 and 3. Hence, the solution in interval notation is (-2, 3).