2c-3(2c-5)-5=(5c+)3c-6

Solution for 2c-3(2c-5)-5=(5c+)3c-6 equation:

2c-3(2c-5)-5=(5c+)3c-6

We move all terms to the left:

2c-3(2c-5)-5-((5c+)3c-6)=0

We add all the numbers together, and all the variables

2c-3(2c-5)-((+5c)3c-6)-5=0

We multiply parentheses

2c-6c-((+5c)3c-6)+15-5=0


We calculate terms in parentheses: -((+5c)3c-6), so:

(+5c)3c-6

We multiply parentheses

15c^2-6

Back to the equation:

-(15c^2-6)


We add all the numbers together, and all the variables

-4c-(15c^2-6)+10=0

We get rid of parentheses

-15c^2-4c+6+10=0

We add all the numbers together, and all the variables

-15c^2-4c+16=0

a = -15; b = -4; c = +16;
Δ = b2-4ac
Δ = -42-4·(-15)·16
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{61}}{2*-15}=\frac{4-4\sqrt{61}}{-30}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{61}}{2*-15}=\frac{4+4\sqrt{61}}{-30}
$