Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  3 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((24•(x3))-(16•(x2)))-(((6•(x3))+(2•32x2))-14)
 Step  2  :

Equation at the end of step  2  :

  ((24•(x3))-(16•(x2)))-(((2•3x3)+(2•32x2))-14)
 Step  3  :

Equation at the end of step  3  :

  ((24 • (x3)) -  24x2) -  (6x3 + 18x2 - 14)
 Step  4  :

Equation at the end of step  4  :

  ((23•3x3) -  24x2) -  (6x3 + 18x2 - 14)

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   18x³ - 34x² + 14  =   2 • (9x³ - 17x² + 7) 

Polynomial Roots Calculator :

 6.2    Find roots (zeroes) of :       F(x) = 9x³ - 17x² + 7
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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  9  and the Trailing Constant is  7.

 The factor(s) are:

of the Leading Coefficient :  1,3 ,9
 of the Trailing Constant :  1 ,7

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  2 • (9x3 - 17x2 + 7)