# Solving a simple equation

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.

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## migrated from physics.stackexchange.comMay 3 '13 at 13:20

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Sounds like you need the quadratic formula. – Mike Dunlavey May 3 '13 at 12:59
The lecturer says that $x$ represents the position of an object moving along a line as a function of time, $t$. About a minute later he asks "At what time will x equal 0?" In other words, for what $t$ value(s) will $8-6t+t^2=0$?. Now look at vadim123's answer. – Rick Decker May 3 '13 at 15:51

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 $t=4$.