3m(3m+6)-3(m^2+4m+1)=0

Solution for 3m(3m+6)-3(m^2+4m+1)=0 equation:

3m(3m+6)-3(m^2+4m+1)=0

We multiply parentheses

9m^2-3m^2+18m-12m-3=0

We add all the numbers together, and all the variables

6m^2+6m-3=0

a = 6; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·6·(-3)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*6}=\frac{-6-6\sqrt{3}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*6}=\frac{-6+6\sqrt{3}}{12}
$