How do you solve by factoring $5n^2- 17n= -6$ ?

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Answer 1 · 2016-05-14T21:41:49

$n = 2/5$ or $n = 3$

First add $6$ to both sides to get:

$5n^2-17n+6 = 0$

Then use an AC method:

Look for a pair of factors of $AC = 5*6 = 30$ with sum $B=17$ .

The pair $15, 2$ works.

Use this pair to split the middle term and factor by grouping:

$5n^2-17n+6$

$= 5n^2-15n-2n+6$

$= (5n^2-15n)-(2n-6)$

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

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

So our original equation becomes:

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

with solutions:

$n = 2/5$ or $n = 3$

How do you solve by factoring 5n^2- 17n= -6 5n^2- 17n= -6?