```Question 89355
In order to factor {{{5*y^2+7*y-6}}}, first multiply 5 and -6 to get -30 and we need to ask ourselves: What two numbers multiply to -30 and add to 7? Lets find out by listing all of the possible factors of -30

Factors:

1,2,3,5,6,10,15,30,

-1,-2,-3,-5,-6,-10,-15,-30, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -30.

(-1)*(30)=-30

(-2)*(15)=-30

(-3)*(10)=-30

(-5)*(6)=-30

Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7

<TABLE><TR><TD>First Number</TD><TD>|</TD><TD>Second Number</TD><TD>|</TD><TD>Sum</TD></TR><TR><TD>1</TD><TD>|</TD><TD>-30</TD>|</TD><TD>|</TD><TD>1+(-30)=-29</TD></TR><TR><TD>2</TD><TD>|</TD><TD>-15</TD>|</TD><TD>|</TD><TD>2+(-15)=-13</TD></TR><TR><TD>3</TD><TD>|</TD><TD>-10</TD>|</TD><TD>|</TD><TD>3+(-10)=-7</TD></TR><TR><TD>5</TD><TD>|</TD><TD>-6</TD>|</TD><TD>|</TD><TD>5+(-6)=-1</TD></TR><TR><TD>-1</TD><TD>|</TD><TD>30</TD>|</TD><TD>|</TD><TD>(-1)+30=29</TD></TR><TR><TD>-2</TD><TD>|</TD><TD>15</TD>|</TD><TD>|</TD><TD>(-2)+15=13</TD></TR><TR><TD>-3</TD><TD>|</TD><TD>10</TD>|</TD><TD>|</TD><TD>(-3)+10=7</TD></TR><TR><TD>-5</TD><TD>|</TD><TD>6</TD>|</TD><TD>|</TD><TD>(-5)+6=1</TD></TR><TABLE>We can see from the table that -3 and 10 add to 7. So the two numbers that multiply to -30 and add to 7 are: -3 and 10

{{{5*y^2+7*y-6}}}

breaks down to this (just replace {{{7*y}}} with the two numbers that multiply to -30 and add to 7, which are: -3 and 10)

{{{5*y^2-3y+10y-6}}}

Group the first two terms together and the last two terms together like this:

{{{(5*y^2-3y)+(10y-6)}}}

Factor a y out of the first group and factor a 2 out of the second group.

{{{y(5y-3)+2(5y-3)}}}

Now since we have a common term {{{5y-3}}} we can combine the two terms.

{{{(y+2)(5y-3)}}} Combine like terms.