how would you slove this equation? y3-5y2=0

Question

how do you slove this problem? solving equations please help

Answer 1

I would factor out y^2.  ---------------> (y-5)y^2=0

Now, I have two possible ways to attain a zero answer ----->  y-5 = 0

                                                                                               y^2 = 0

Solve for y ----------------------------->  y-5 = 0

                                                                y-5+5 = 0 +5

                                                                y-0 = 5

                                                                y = 5

Solve for y ---------------------------->  y^2 = 0

                                                               y = 0

Therefore, the answer is:  The set of 0 and 5 equals y. 

Answer 2

This equation has 2 roots. To find them we have to simplify equation. Remember that y^3=y·y·y=y·y^2 ; So the greatest common factor is y^2 , and we will move it out of parentheses (distributive property)
y^2(y-5)=0.
Product equal to zero if at least one factor is zero. Because both factors contain a variable, let's assume that
1. y=0 then 0·(0-5)=0 (true statement)
or
2. y-5=0 → y=5
The answer is set of two numbers 0 and 5
{0 , 5}
Of cause, it is important check you answers.

Answer 3

Error. Apology...Twenty characters to comply with editing demands.

Answer 4

I would first find the greatest common factor between y^3 and y^2. It is y^2

Then I would re-write the problem with y^2 factored out.

1) Original  : y^3 - 5y^2=0 

2) Factored: y^2 (y-5)=0

Next I would divide both sides of the equal sign by y^2 to get

3) y-5=0

Then add 5 to both sides of equation to get

4) y=5 

After solving the problem and checking the answer, stop and reflect upon why the answer is 5. Also is there any other number for y  that could be used to satisfy the equation? Also, why is 5 the only number greater than zero that will satisfy the equation?