The coefficient of x² is 2 and the constant term is -3. The product of 2 and -3 is -6. So, the factors of -6 which sum to 5 are -1 and 6, therefore:
[tex]2x^2+5x-3=2x^2+6x-x-3=3(2x-1)+x(2x-1)[/tex]Factor 2x-1 from the previous expression:
[tex](2x-1)(3+x)[/tex]