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

#8k - color(red)(3)(k - 5) = 45#

#8k - (color(red)(3) xx k) - (color(red)(3) xx -5) = 45#

#8k - 3k - (-15) = 45#

#8k - 3k + 15 = 45#

#(8 - 3)k + 15 = 45#

#5k + 15 = 45#

Next, subtract #color(red)(15)# from each side of the equation to isolate the #k# term while keeping the equation balanced:

#5k + 15 - color(red)(15) = 45 - color(red)(15)#

#5k + 0 = 30#

#5k = 30#

Now, divide each side of the equation by #color(red)(5)# to solve for #k# while keeping the equation balanced:

#(5k)/color(red)(5) = 30/color(red)(5)#

#(color(red)(cancel(color(black)(5)))k)/cancel(color(red)(5)) = 6#

#k = 6#