What is the solution set of the equation...?

Question

2x2=3x-2=0

by the way, the 2x2 should be 2x squared.

how do i solve this?

Answer 1

Hmmm...I don't know how to solve that expression with two equal signs.  Did you mean to put a + symbol instead of the first = sign?  I'm going to assume you did and solve that problem instead.

2x² + 3x - 2 = 0

You want to factor this polynomial.  Since the x² term has a coefficient of 2, you know that if it factors it will be in the form (2x + a)(x + b) where a and b are constants.  You also know that a*b = -2 and that 2b + a = 3.  Since a*b = -2, either a is positive and b is negative or visa versa.  I get the following factorization:

(2x - 1)(x + 2) = 0

Answer:  x = -2 or x = ½

Hope this helps you!