(12k+3)(3k-10)=0

Solution for (12k+3)(3k-10)=0 equation:

(12k+3)(3k-10)=0

We multiply parentheses ..

(+36k^2-120k+9k-30)=0

We get rid of parentheses

36k^2-120k+9k-30=0

We add all the numbers together, and all the variables

36k^2-111k-30=0

a = 36; b = -111; c = -30;
Δ = b2-4ac
Δ = -1112-4·36·(-30)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-129}{2*36}=\frac{-18}{72}
=-1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+129}{2*36}=\frac{240}{72}
=3+1/3
$