(3c+2)(2c-7)=180

Solution for (3c+2)(2c-7)=180 equation:

(3c+2)(2c-7)=180

We move all terms to the left:

(3c+2)(2c-7)-(180)=0

We multiply parentheses ..

(+6c^2-21c+4c-14)-180=0

We get rid of parentheses

6c^2-21c+4c-14-180=0

We add all the numbers together, and all the variables

6c^2-17c-194=0

a = 6; b = -17; c = -194;
Δ = b2-4ac
Δ = -172-4·6·(-194)
Δ = 4945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{4945}}{2*6}=\frac{17-\sqrt{4945}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{4945}}{2*6}=\frac{17+\sqrt{4945}}{12}
$