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.