How do you factor the trinomial $12 k^{2} + 15 k = 16 k + 20$ $12k^2+15k=16k+20$ ?

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Answer 1 · 2015-11-18T22:39:51

The factors are: $(3 k - 4) (4 k + 5)$ $(3k - 4)(4k+ 5)$

$12 k^{2} - k - 20 = 0$ $12k^2-k-20=0$
Integer factors of 12 are: {1,12} , {2,6}, {3,4}

Integer factors of 20 are: {1,20}, {2,10}, {4,5}

The combination that could yield $12 k^{2}$ $12k^2$ and $k$ $k$ are
{3,4} for 12 and {4,5} for 20

Try-1
$(3 k - 4) (4 k + 5) = 12 k^{2} + 15 k - 16 k - 20$ $(3k - 4)(4k+ 5) =12k^2 +15k -16k -20$

$Struck lucky first try!$ $color(green)("Struck lucky first try!")$

$12 k^{2} + 15 k = 16 k + 20 \times \to \times (3 k - 4) (4 k + 5) = 0$ $12k^2+15k=16k+20 color(white)(xx) -> color(white)(xx)(3k - 4)(4k+ 5)=0$

How do you factor the trinomial 12k^2+15k=16k+2012k2+15k=16k+2012k^2+15k=16k+20?