How to solve $\left(\frac3{p-3}-1\right)\left(2+\frac4{p-2}\right)=0$?

Question

I'm currently preparing myself for uni and thus learning on my own. This equation is killing me as the book doesn't explain how to solve it.

$$\left(\frac3{p-3}-1\right)\left(2+\frac4{p-2}\right)=0$$

Answer 1

By the null factor law, if $xy=0$ then $x=0$ or $y=0$. Apply this to your equation and you'll get two answers.

Answer 2

By Null -Factor law, If xy = 0 , Then, either x = 0 or y = 0.

Hence, applying this property in this given equation : We get ,

Equate both terms on Left side factor and Right side factor of left hand side equation to $0$ $$p-3 = \frac 31 \implies p = 6$$ Or :
$$p-2= -2 \implies p = 0$$ So, either $p = 0$ or $p = 6$