First, expand the terms within parenthesis on the right side of the equation by multiplying each term within the parenthesis by color(red)(-3)−3:
42 = color(red)(-3)(6 + v)42=−3(6+v)
42 = (color(red)(-3)xx6) + (color(red)(-3)xxv)42=(−3×6)+(−3×v)
42 = -18 - 3v42=−18−3v
Next, add color(red)(18)18 to each side of the the equation to isolate the vv term while keeping the equation balanced:
color(red)(18) + 42 = color(red)(18) - 18 - 3v18+42=18−18−3v
60 = 0 - 3v60=0−3v
60 = -3v60=−3v
Now, divide each side of the equation by color(red)(-3)−3 to solve for vv while keeping the equation balanced:
60/color(red)(-3) = (-3v)/color(red)(-3)60−3=−3v−3
-20 = (color(red)(cancel(color(black)(-3)))v)/cancel(color(red)(-3))
-20 = v
v = -20
