Solving a simple equation

Question

I am just starting to study physics and I found this equation:

$$\ x = 8 - {6t} + t^2$$

If possible please explain in a step by step.

Sorry if it's too simple.

Answer 1

We rewrite $x=8-6t+t^2=t^2-6t+8=(t-2)(t-4)$, where the last step is obtained by factoring. Assuming you want to solve $x=0$, then either $t-2=0$ or $t-4=0$. This leads to the two solutions $t=2$ and $t=4$.