A2+2a-3=0 solving equations by completing the square

I assume that you mean a^2 + 2a - 3 = 0

You need to find two numbers that multiply together to give the number 3 and when added give the answer 2 (as in 2a).  In this case the numbers are 3 and 1 (3 x 1 = 3 and 3 - 1 = 2)

Therefore we have
(a + 3)(a - 1) = 0

The values of x which solve the equation are -3 and 1
The reason is that -3 + 3 = 0 and 1 - 1 = 0 : zero times any number is zero