How do you solve #8n ^ { 2} + 56n = - 48#?

1 Answer
Jan 14, 2018

#8n^2+56n= -48#
#8n^2+56n+48=0#

Divide by 8 throughout #\implies#

#n^2+7n+6 = 0#

Now you factorize 6 and look for the combination that results in +6 and has a sum of +7.

We have the following pairs of roots#(1,6),(-1,-6),(3,2),(-3,-2)# that give +6. The first set gives the sum of +7. So the equation can be written as

#n^2+n+6n+6 = 0#
#n(n+1)+6(n+1) = 0#
#(n+1)(n+6) = 0#
#n = -1,-6#