First, expand the term within parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#15 + 6n = 7(2n + 3)#

#15 + 6n = (7 xx 2n) + (7 xx 3)#

#15 + 6n = 14n + 21#

Next, subtract #color(red)(6n)# and #color(blue)(21)# from each side of the equation to isolate the #n# term while keeping the equation balanced:

#15 + 6n - color(red)(6n) - color(blue)(21) = 14n + 21 - color(red)(6n) - color(blue)(21)#

#15 - color(blue)(21) + 6n - color(red)(6n) = 14n - color(red)(6n) + 21 - color(blue)(21)#

#-6 + 0 = 8n + 0#

#-6 = 8n#

Now, divide each side of the equation by #color(red)(8)# to solve for #n# while keeping the equation balanced:

#-6/color(red)(8) = (8n)/color(red)(8)#

#-6/8 = (color(red)(cancel(color(black)(8)))n)/cancel(color(red)(8))#

#-(2 xx 3)/(2 xx 4) = n#

#-(color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 4) = n#

#-3/4 = n#

#n = -3/4#