First step is to expand the terms within the parenthesis:
#x(1 - x) + 2x - 4 = 8x - 24 - x^2#
#x - x^2 + 2x - 4 = 8x - 24 - x^2#
We can now group and combine like terms:
#x + 2x - x^2 - 4 = 8x - 24 - x^2#
#3x - x^2 - 4 = 8x - 24 - x^2#
We can now add and subtract the necessary terms to isolate the #x# terms while keeping the equation balanced:
#3x - x^2 - 4 - color(red)(3x) + color(blue)(x^2) + color(green)(24) = 8x - 24 - x^2- color(red)(3x) + color(blue)(x^2) + color(green)(24)#
#3x - color(red)(3x) - x^2 + color(blue)(x^2) - 4 + color(green)(24) = 8x - color(red)(3x) - 24 + color(green)(24) - x^2 + color(blue)(x^2)#
#0 - 0 - 4 + color(green)(24) = 8x - color(red)(3x) - 0 - 0#
#- 4 + color(green)(24) = 8x - color(red)(3x)#
#20 = 5x#
Now we can divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:
#20/color(red)(5) = (5x)/color(red)(5)#
#4 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))#
#4 = x#
#x = 4#
