(m4)(3m10)=3(m2)+18
∴ 3m^{2} 10m 12m +40 = 3m  6 + 18
3m^{2} 22m + 40 = 3m + 12
3m^{2}  25m + 28 = 0
which is in the form ax^{2} + bx +c = 0
In this case a = 3; b = 25 and c = 28
m = [b ± (b^{2}  4ac)^{½}]/2a
m = {25 ± [(25)^{2 } 4(3)(28)]^{½}}/(2)(3)
m = {25 ± [625  336]^{½}}/6
m = [25 ± 17]/6
m = [25  17]/6 = 8/6 = 1.333 and m = [25 + 17]/6 = 7
CHECK: Substituting m = 7 back into the original equations:
Does (7  4)[(3(7)  10] = 3(7  2) + 18?
(3)(11) = 3(5) + 18?
YES!
Why don't you try substituting m = 1.3333 back into the original equations to see if it also "works."
10/12/2013

William S.