(5c-3)(6c-1)=0

Solution for (5c-3)(6c-1)=0 equation:

(5c-3)(6c-1)=0

We multiply parentheses ..

(+30c^2-5c-18c+3)=0

We get rid of parentheses

30c^2-5c-18c+3=0

We add all the numbers together, and all the variables

30c^2-23c+3=0

a = 30; b = -23; c = +3;
Δ = b2-4ac
Δ = -232-4·30·3
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*30}=\frac{10}{60}
=1/6
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*30}=\frac{36}{60}
=3/5
$