We are trying to solve this equation
[tex]7r^{2} -41r-6=0[/tex]
We need to split up -41r in order to factor by grouping. We need to spilt -41r into 2, where one can be factored with [tex]7r^{2}[/tex] and other part can be factored with -6.
We can find out how to split it by multipling 7 and -6 to get -42. We need to split -41 where it can be multiplied to get -42. It is -42 and 1.
[tex]7r^{2} +r-42r-6=0[/tex]
We can then factor by grouping them
With [tex]7r^{2}[/tex] and r, they can factor out a r.
With -42r and -6, they can factor out a -6.
So it will be [tex]r(7r+1)-6(7r+1)=0[/tex]
Notice that inside the parenthesizes, both are 7r+1, we want it to be the same.
We can arrange it into (r-6)(7r+1)=0
We need to find what values of r would make the equation equal to 0.
Multiplying anything by 0 will equal 0, so there will be 2 solutions.
For (r-6), if r=6 then the equation will = 0
For (7r+1), if r = -1/7 then the equation will = 0.
So the solution will be r= -1/7, 6
