Solve? $3n^2-2n+1=-3n^2+9n+11$

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Answer 1 · 2017-02-26T11:28:09

$n=-2/3, 5/2$

We have (I think I've got this right...)

$3n^2-2n+1=-3n^2+9n+11$

Let's set the whole thing equal to 0:

$6n^2-11n-10=0$

I'll try first to factor it into a form of $(ax+b)(cx+d)$ such that:

I'll do it in a chart format:

$((a,b,c,d,ac,bd,ad,bc,ad+bc),(3,2,2,-5,6,-10,-15,4,-11))$

(first crack - got lucky!)

And so our factoring is:

$(3n+2)(2n-5)=0$

$n=-2/3, 5/2$

We can see these points of intersection in the graph:

graph{(y-(3x^2-2x+1))(y-(-3x^2+9x+11))=0 [-10, 10, -14.42, 20]}

Solve? 3n^2-2n+1=-3n^2+9n+113n^2-2n+1=-3n^2+9n+11