Final answer:
To solve the equation 2x²+5x-3=0 by factoring, we find two numbers whose product is equal to the product of the coefficient of x² and the constant term. Then, we set each factor equal to zero to find the values of x, which are 1/2 and -3.
Step-by-step explanation:
To solve the equation 2x²+5x-3=0 by factoring, we need to find two numbers whose product is equal to the product of the coefficient of x² and the constant term. In this case, the coefficient of x² is 2 and the constant term is -3, so we need to find two numbers whose product is -6 and whose sum is equal to the coefficient of x, which is 5.
The numbers that satisfy these conditions are 6 and -1. We can then rewrite the equation as (2x-1)(x+3) = 0 and set each factor equal to zero to find the values of x. So, we have 2x-1=0 and x+3=0. Solving these equations gives us x=1/2 and x=-3.