SOLUTION: Can anyone explain why 8y(y-2)=0 = (y=0,y=2) I tried the problem solver, but I don't get it. Thanks.

Question 917751: Can anyone explain why 8y(y-2)=0 = (y=0,y=2) I tried the problem solver, but I don't get it. Thanks.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if a * b = 0 then either a = 0 or b = 0 or both = 0.
have to be, otherwise the result will not be 0.

take that concept and apply it to 8y * (y-2) = 0

let a = 8y
let b = (y-2)

a * b = 0 becomes 8y * (y-2) = 0

then either 8y = 0 or (y-2) = 0, otherwise the result will not be 0.

solve each for 0.

8y = 0 results in y = 0 when you solve for y.

y-2 = 0 results in y = 2 when you solve for y.

confirm your results by substituting in the original equation.

original equation is 8y * (y-2) = 0

when y = 0, this becomes 0 * -2 = 0 which becomes 0 = 0 which is true.

when y = 2, this becomes 16 * 0 = 0 which becomes 0 = 0 which is true.

the original equation holds true when y = 0 or when y = 2.

that confirms the solution is correct.

solver handled this no problem.

i entered 8y(y-2)=0

i also entered 8y*(y-2)=0

it handled both easily and said the solution was y = 0 or 2.

the explanations it gave under "detailed" may not be the best.

in fact, i had trouble understanding exactly what they were talking about.

if that's what you meant as to why you didn't get it, then i agree.

the reason is as i stated above.

if a * b = 0 then either a has to be equal to 0 or b has to be equal to 0 in order for the result to be equal to 0.

both factors can also be equal to 0 at the same time, but that only occurs in special circumstances when the factors are either the same or mu;ltiples of each other.

example:

(y-2) * (y-2) = 0
both factors are equal to 0 when y = 2.

example again:
(y-2) * (2y-4) = 0
both factors are equal to 0 when y = 2

having both factors equal to 0 at the same time is not essnetial. only one of the factors has to be 0 in order for the result to be equal to 0.

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