6m(-2m+6)+4=10

Solution for 6m(-2m+6)+4=10 equation:

6m(-2m+6)+4=10

We move all terms to the left:

6m(-2m+6)+4-(10)=0

We add all the numbers together, and all the variables

6m(-2m+6)-6=0

We multiply parentheses

-12m^2+36m-6=0

a = -12; b = 36; c = -6;
Δ = b2-4ac
Δ = 362-4·(-12)·(-6)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{7}}{2*-12}=\frac{-36-12\sqrt{7}}{-24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{7}}{2*-12}=\frac{-36+12\sqrt{7}}{-24}
$