Step 1) Add the necessary values to each side of the equation to isolate the #x# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:
#4x + 16 - color(red)(4x) + color(blue)(32) = 8x - 32 color(red) - color(red)(4x) + color(blue)(32)#
Group and combine like terms on each side of the equation:
#4x - color(red)(4x) + 16 + color(blue)(32) = 8x - color(red)(4x) - 32 color(red) + color(blue)(32)#
#0 + 16 + 32 = 8x - 4x - 0#
#48 = 4x#
Now we can divide each side of the equation by #color(red)(4)# to solve for #x# while keeping the equation balanced:
#48/color(red)(4) = (4x)/color(red)(4)#
#12 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))#
#12 = x#
#x = 12#
