Find the roots of 2x^2 + 5x - 12 = 0

Problem: Find the roots of the quadratic equation $2x^2 + 5x - 12 = 0$.

Steps

1. Factor the quadratic expression
   $$(2x - 3)(x + 4) = 0$$
2. Apply the zero product property
   $$2x - 3 = 0 \quad \text{or} \quad x + 4 = 0$$
3. Solve the first linear equation
   $$x = \frac{3}{2}$$
4. Solve the second linear equation
   $$x = -4$$