I was checking out the steps for a math problem when I saw something that didn\'

Question

I was checking out the steps for a math problem when I saw something that didn't make any sense (to me at least). Here are the steps (all steps are correct).

PROBLEM: Solve for t. Assume that t equals 0 is not a solution (t=/=0).

-4.9(t^2) + 5t + 100 = 100

STEP 1: -4.9(t^2) + 5t = 0

STEP 2: t(-4.9t + 5) = 0

STEP 3: t = 0 is not an option. Therefore,

                -4.9t + 5 = 0

STEP 4: -4.9t = -5

STEP 5: t = -5/-4.9

STEP 6: t = 1.02

My problem is that I don't understand step 3. How is it acceptable to remove the t in t(-4.9 + 5) = 0.

I want to understand the mechanism and reasoning behind this. I understand 1.02 is the solution for t (all I have to do is plug in 1.02 for t to prove that)  but I want to know why step 3 was okay. If there is some sort of mathematical law that I don't know about that makes step 3 make sense then I want to know its name and how it works in clear detail so that I can use it on my own for the future. Please explain.

Explanation / Answer

You aren't removing t, you are setting each factor separately equal to 0. Formally, this is called "Zero Factor Law" or "Zero Factor Property": If ab = 0, then a = 0 or b = 0.

t(-4.9t + 5) = 0

Then by Zero Factor Property:

t = 0 or -4.9t + 5 = 0

But they told you that t = 0 is not a solution so that is why t = 0 is dropped.

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