First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
#color(red)(-5)(v + 2) + 3v + 6 = 8v + 9#
#(color(red)(-5) xx v) + (color(red)(-5) xx 2) + 3v + 6 = 8v + 9#
#-5v + (-10) + 3v + 6 = 8v + 9#
#-5v - 10 + 3v + 6 = 8v + 9#
Next, group and combine like terms on the left side of the equation:
#-5v + 3v - 10 + 6 = 8v + 9#
#(-5 + 3)v - 4 = 8v + 9#
#-2v - 4 = 8v + 9#
Then, add #color(red)(2v)# and subtract #color(blue)(9)# from each side of the equation to isolate the #v# term while keeping the equation balanced:
#-2v + color(red)(2v) - 4 - color(blue)(9) = 8v + color(red)(2v) + 9 - color(blue)(9)#
#0 - 13 = (8 + color(red)(2))v + 0#
#-13 = 10v#
Now, divide each side of the equation by #color(red)(10)# to solve for #v# while keeping the equation balanced:
#-13/color(red)(10) = (10v)/color(red)(10)#
#-13/color(red)(10) = (color(red)(cancel(color(black)(10)))v)/cancel(color(red)(10))#
#-13/color(red)(10) = v#
#v = -13/color(red)(10)#
Or
#v = -1.3#
