Question

How to solve this step by step solution 3n^2 - 129n + 1386 = 0?

Answer 1

Answer: n=21 or n=22

Step-by-step explanation:

3n^2 - 129n + 1386 = 0

⇒3(n²-43n+462)=0

⇒n²-43n+462=0 _____(i)

⇒Now, 462 =3*2*7*11=(7*3)*(2*11)=(21)*(22)=(-21)(-22)

⇒ Also, -43 = -21 -22

⇒Now (i)⇒n²-43n+462=0

⇒n²-21n-22n+462=0

⇒n²-21n-22n+(21*22)=0

⇒n(n-21)-22(n-21)=0

⇒(n-21)(n-22)=0

⇒n=21 (or) n=22

Answer 2

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Here is your answer
$3n {}^{2} - 129n + 1386 = 0 \\ divided \: by \: 3 \: we \: get \\ n {}^{2} - 43n + 462 = 0 \\ n {}^{2} - 22n - 21n + 462 = 0 \\ n(n - 22) - 21(n - 22) = 0 \\ (n - 22)(n - 21) = 0 \\ n - 22 = 0 \\ n = 22 \\ and \\ n - 21 = 0 \\ n = 21$
Therefore
n = 22 and 22

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