Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3•52t2) +  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   75t² + 12  =   3 • (25t² + 4) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(t) = 25t² + 4
Polynomial Roots Calculator is a set of methods aimed at finding values of  t  for which   F(t)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  t  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  25  and the Trailing Constant is  4.

 The factor(s) are:

of the Leading Coefficient :  1,5 ,25
 of the Trailing Constant :  1 ,2 ,4

 Let us test ....

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

  3 • (25t2 + 4)