solve by factoring 2a^2-3a=-5

2a^2 - 3a = -5

2a^2 - 3a + 5 = 0 does not factor.

To factor, find the two factors of each of the end terms that will sum to the middle value.

Are you sure that you don't have a typo?

2a^2 - 3a - 5 = 0

(2a - 5)(a + 1) = 0

a = -1, 5/2