Which equation is equivalent y= 3x^2-15x+18

Two solutions were found :

x = 6

x = -1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (3x2 -  15x) -  18  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  3x2 - 15x - 18  =   3 • (x2 - 5x - 6)  

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 5x - 6  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    x2 - 6x + 1x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-6)

            Which is the desired factorization

Equation at the end of step  3  :

 3 • (x + 1) • (x - 6)  = 0

In Conclusion, the answer would be 0.

step-by-step explanation: