Solve the following equation: 11x + 8x^2 - 3 = 3x^2 + 6x + 7

Let's solve the equation step by step: 1. Rewrite the equation: $$11x + 8x^2 - 3 = 3x^2 + 6x + 7$$ 2. Move all terms to one side: $$8x^2 - 3x^2 + 11x - 6x - 3 - 7 = 0$$ 3. Combine like terms: $$5x^2 + 5x - 10 = 0$$ 4. Simplify the equation by dividing by 5: $$x^2 + x - 2 = 0$$ 5. Solve the quadratic equation. We can use factoring: We need to find two numbers that multiply to -2 and add up to 1. These numbers are 2 and -1. $$(x + 2)(x - 1) = 0$$ 6. Set each factor equal to zero and solve for x: $$x + 2 = 0 \Rightarrow x = -2$$ $$x - 1 = 0 \Rightarrow x = 1$$ Therefore, the solutions are x = -2 and x = 1. Answer: x = -2, x = 1