First, expand the term in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis;
#4k + 4 = color(red)(-6)(6k + 6)#
#4k + 4 = (color(red)(-6) xx 6k) + color(red)(-6) xx 6)#
#4k + 4 = -36k - 36#
Next, subtract #color(red)(4)# and add #color(red)(36k)# to each side of the equation to isolate the #k# term while keeping the equation balanced:
#color(red)(36k) + 4k + 4 - color(red)(4) = color(red)(36k) - 36k - 36 - color(red)(4)#
#(color(red)(36) + 4)k + 0 = 0 - 40#
#40k = -40#
Now, divide each side of the equation by #color(red)(40)# to solve for #k# while keeping the equation balanced:
#(40k)/color(red)(40) = -40/color(red)(40)#
#(color(red)(cancel(color(black)(40)))k)/cancel(color(red)(40)) = -1#
#k = -1#
