Given: #8m^2 + 20m = 12#
First put the equation in #Ax^2 + Bx + C = 0# form.
#8m^2 + 20m - 12 = 0#
Next factor the greatest common factor (GCF) from each term:
#4(2m^2 + 5m - 3) = 0#
The factored equation will look like this: #4(2m + x)(m + y) = 0#
Now find two numbers #x, y# that multiply to #-3#:
#-3 and 1 " or " -1 and 3#.
Middle term using distribution will be: # x + 2y = 5#.
Let #x = 1, y = -3: " "2(-3) + 1 = -5" "# Doesn't work
Let #x = -3, y = 1: " "2(1) + (-3) = -1 " "# Doesn't work
Let #x = 3, y = -1: " "2(-1) + 3 = 1 " "# Doesn't work
Let #x = -1, y = 3: " "2(3) + (-1) = 5 " " # WORKS!
#4 (2m -1)(m + 3) = 0#
The two factors that make the equation #= 0# are:
#2m - 1 = 0 " and " m + 3 = 0#
#2m = 1 " and " m = -3#
#m = 1/2 " and " m = -3#
