Answer:
y= -2/5 and y=1
Step-by-step explanation:
Start by transforming the equation to your liking:
[tex]5y^2-2=3y\\5y^2-3y-2=0\\[/tex]
Now we have to factor! To do this we have to find common numbers. Do this by multiplying -2 and 5 to get -10. Now think about which two numbers add multiply to be -10 but also add up to be -3 (I got this number from the middle of the equation). The two numbers you should've got are -5 and 2.
Now substitute those two number in place of the middle term, which is -3y like so:
[tex]5y^2-5y+2y-2 =0[/tex]
Now solve the equation in pieces... find the greatest common factor from [tex](5y^2-5y)[/tex] and the greatest common factor from [tex](2y-2)[/tex] . The two common factors for both of those are 5y and 2. Your equation should now look like this:
[tex]5y(y-1)[/tex] + [tex]2(y-1)[/tex]
The two greatest common factors become into one group and the other equation that they have in common (y-1) is it's own equation:
[tex](5y+2)(y-1)=0[/tex]
Now equal both of the equations to 0 and solve for y to get both of the values of y.
