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

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

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

We multiply parentheses ..

(+30c^2+25c-18c-15)=0

We get rid of parentheses

30c^2+25c-18c-15=0

We add all the numbers together, and all the variables

30c^2+7c-15=0

a = 30; b = 7; c = -15;
Δ = b2-4ac
Δ = 72-4·30·(-15)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-43}{2*30}=\frac{-50}{60}
=-5/6
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+43}{2*30}=\frac{36}{60}
=3/5
$