First, subtract #color(red)(21m)# and add #color(blue)(108)# to both sides of the equation to form a quadratic on the left side of the equation while keeping the equation balanced:
#m^2 - color(red)(21m) + color(blue)(108) = 21m - 108 - color(red)(21m) + color(blue)(108)#
#m^2 - 21m + 108 = 21m - color(red)(21m) - 108 + color(blue)(108)#
#m^2 - 21m + 108 = 0 - 0#
#m^2 - 21m + 108 = 0#
Next, factor the quadratic on the left side of the equation as:
#(m - 12)(m - 9) = 0#
Now, solve each term on the left side of the equation for #0#:
Solution 1)
#m - 12 = 0#
#m - 12 + color(red)(12) = 0 + color(red)(12)#
#m - 0 = 12#
#m = 12#
Solution 2)
#m - 9 = 0#
#m - 9 + color(red)(9) = 0 + color(red)(9)#
#m - 0 = 9#
#m = 9#
The solution is: #m = 12# and #m = 9#
