Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "c2"   was replaced by   "c^2".  2 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

         (c3)
  (0-((6•————)•(c4)))+23c2
          2  
 Step  2  :
            c3
 Simplify   ——
            2 

Equation at the end of step  2  :

              c3             
  (0 -  ((6 • ——) • c4)) +  23c2
              2              

Step  3  :

Multiplying exponential expressions :

 3.1    c³ multiplied by c⁴ = c^{(3 + 4)} = c⁷

Equation at the end of step  3  :

  (0 -  3c7) +  23c2

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   8c² - 3c⁷  =   -c² • (3c⁵ - 8) 

Polynomial Roots Calculator :

 5.2    Find roots (zeroes) of :       F(c) = 3c⁵ - 8
Polynomial Roots Calculator is a set of methods aimed at finding values of  c  for which   F(c)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  c  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  -8.

 The factor(s) are:

of the Leading Coefficient :  1,3
 of the Trailing Constant :  1 ,2 ,4 ,8

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  -c2 • (3c5 - 8)