Evaluate a+2b.

Suppose that there exist two positive real numbers $a$ and $b$ such that $(a-2) (a^2+2a-18)+ab(2a+b+18)-96+2(b-2)(b+3)(b+2)=0$.

Evaluate $a+2b$.

My solution:

Learning Algebraic Manipulation Skills

Some algebraic manipulation skills that you could learn by watching me doing it and it is going to be very rewarding if you know when to utilize these skills and use them to your advantage.

I'm sure you're pretty familiar with factoring sum and difference of squares or even cubes and recognizing perfect squares at first glance, take for example, when you see