(6a+42)(18a-12)=0

Solution for (6a+42)(18a-12)=0 equation:

(6a+42)(18a-12)=0

We multiply parentheses ..

(+108a^2-72a+756a-504)=0

We get rid of parentheses

108a^2-72a+756a-504=0

We add all the numbers together, and all the variables

108a^2+684a-504=0

a = 108; b = 684; c = -504;
Δ = b2-4ac
Δ = 6842-4·108·(-504)
Δ = 685584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{685584}=828$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(684)-828}{2*108}=\frac{-1512}{216}
=-7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(684)+828}{2*108}=\frac{144}{216}
=2/3
$