(3c-2)(8c+5)=0

Solution for (3c-2)(8c+5)=0 equation:

(3c-2)(8c+5)=0

We multiply parentheses ..

(+24c^2+15c-16c-10)=0

We get rid of parentheses

24c^2+15c-16c-10=0

We add all the numbers together, and all the variables

24c^2-1c-10=0

a = 24; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·24·(-10)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*24}=\frac{-30}{48}
=-5/8
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*24}=\frac{32}{48}
=2/3
$