SOLUTION: What is the equation by factoring 3x^2 = 75x

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Question 181328This question is from textbook Algebra 2
: What is the equation by factoring 3x^2 = 75x This question is from textbook Algebra 2

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given 3x%5E2+=+75x
Most folks would say
Divide both sides by 3
x%5E2+=+25x
Divide both sides by x
x+=+25
What you should do is this
3x%5E2+=+75x
3x%5E2+-+75x+=+0
3x%28x+-+25%29+=+0
So either 3x = 0 OR x-25 = 0
Thus x =0 and x=25 both work
Why doesn't the first thing we did give the same answer? Think about what happens when you 'divide both sides by x'. What does that imply? What happens if x=0.