what are the solutions of the equation 4x² + 3x = 24 - x?\n-3, 2, or 4\n-3 or 2\n-2, 3, or 4\n-2 or 3

Explanation:

Step1: Rearrange to standard quadratic form

First, move all terms to one - side of the equation. [4x^{2}+3x+x - 24=0] [4x^{2}+4x - 24 = 0] Divide through by 4 to simplify: [x^{2}+x - 6=0]

Step2: Factor the quadratic equation

We need to find two numbers that multiply to - 6 and add up to 1. The numbers are 3 and - 2. So, (x^{2}+x - 6=(x + 3)(x - 2)=0)

Step3: Solve for x

Set each factor equal to zero: If (x+3 = 0), then (x=-3) If (x - 2=0), then (x = 2)

Answer:

B. (-3) or (2)