3(c+3)+4c(c+3)=0

Solution for 3(c+3)+4c(c+3)=0 equation:

3(c+3)+4c(c+3)=0

We multiply parentheses

4c^2+3c+12c+9=0

We add all the numbers together, and all the variables

4c^2+15c+9=0

a = 4; b = 15; c = +9;
Δ = b2-4ac
Δ = 152-4·4·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*4}=\frac{-24}{8}
=-3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*4}=\frac{-6}{8}
=-3/4
$