(6m+7)(9m+7)=0

Solution for (6m+7)(9m+7)=0 equation:

(6m+7)(9m+7)=0

We multiply parentheses ..

(+54m^2+42m+63m+49)=0

We get rid of parentheses

54m^2+42m+63m+49=0

We add all the numbers together, and all the variables

54m^2+105m+49=0

a = 54; b = 105; c = +49;
Δ = b2-4ac
Δ = 1052-4·54·49
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-21}{2*54}=\frac{-126}{108}
=-1+1/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+21}{2*54}=\frac{-84}{108}
=-7/9
$