Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (0 -  3x2) -  378

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -3x² - 378  =   -3 • (x² + 126) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(x) = x² + 126
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  1  and the Trailing Constant is  126.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2 ,3 ,6 ,7 ,9 ,14 ,18 ,21 ,42 , etc

 Let us test ....

Note - For tidiness, printing of 15 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

  -3 • (x2 + 126)