27=-3c(6-2c)

Solution for 27=-3c(6-2c) equation:

27=-3c(6-2c)

We move all terms to the left:

27-(-3c(6-2c))=0

We add all the numbers together, and all the variables

-(-3c(-2c+6))+27=0


We calculate terms in parentheses: -(-3c(-2c+6)), so:

-3c(-2c+6)

We multiply parentheses

6c^2-18c

Back to the equation:

-(6c^2-18c)


We get rid of parentheses

-6c^2+18c+27=0

a = -6; b = 18; c = +27;
Δ = b2-4ac
Δ = 182-4·(-6)·27
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{3}}{2*-6}=\frac{-18-18\sqrt{3}}{-12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{3}}{2*-6}=\frac{-18+18\sqrt{3}}{-12}
$