Solve for x : x2 + 5x - (a2+a-6) = 0

Problem : Solve for x : x² + 5x - (a²+a-6) = 0

Doubt by Muskan

Solution : 

First of all lets factorise a²+a-6

= a² + a - 6
= a² + (3-2)a - 6
= a² +3a - 2a - 6
= a(a+3) - 2(a+3)
= (a-2)(a+3)

Now
x² + 5x - (a²+a-6) = 0x² + 5x - (a+3)(a-2) = 0
x² + [(a+3)-(a-2)]x -(a+3)(a-2) = 0
x² + (a+3)x - (a-2)x -(a+3)(a-2) = 0
x [x + (a+3)] -(a-2)[x + (a+3)] = 0
[x + (a+3)] [x - (a-2)] = 0

x + (a+3) = 0
x = -(a+3)

OR

x - (a-2) = 0
x = (a-2) 

∴ x = -(a+3), (a-2)