Question 917751
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.