First, expand the terms within the parenthesis by multiplying each term inside the parenthesis by the term outside the parenthesis while paying close attention to the signs of each term:
#-8 = (color(red)(-4) xx -5) + (color(red)(-4) xx r) + (color(blue)(-4) xx r) + (color(blue)(-4) xx 3)#
#-8 = (+20) + (-4r) + (-4r) + (-12)#
#-8 = 20 - 4r - 4r - 12#
Now we can group and combine like terms on the right side of the equation:
#-8 = 20 - 12 - 4r - 4r#
#-8 = 8 + (-4 - 4)r#
#-8 = 8 + (-8r)#
#-8 = 8 - 8r#
Next we can subtract #color(blue)(8)# from each side of the equation to isolate the #r# term while keeping the equation balanced:
# - color(blue)(8) - 8 = -color(blue)(8) + 8 - 8r#
#-16 = 0 - 8r#
#-16 = -8r#
Finally, we can divide each side of the equation by #color(red)(-8)# to solve for #r# while keeping the equation balanced:
#(-16)/color(red)(-8) = (-8r)/color(red)(-8)#
#(cancel(-)16)/color(red)(cancel(-)8) = (color(red)(cancel(color(black)(-8)))r)/cancel(color(red)(-8))#
#16/color(red)(8) = r#
#2 = r#
#r = 2#
