(10 - 10y) - 10y = y²- 18 + 4y

y = − 12 + 2 √ 43 , − 12 - 2√ 43

Step-by-step explanation:

 2⋅(y+3)⋅(y−6)

Exsplanation

2

1

See steps

Step by Step Solution:

More Icon

STEP

1

:

                10y    

Simplify   ————————————

           y2 - 3y - 18

Trying to factor by splitting the middle term

1.1     Factoring  y2 - 3y - 18

The first term is,  y2  its coefficient is  1 .

The middle term is,  -3y  its coefficient is  -3 .

The last term, "the constant", is  -18

Step-1 : Multiply the coefficient of the first term by the constant   1 • -18 = -18

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -3 .

     -18    +    1    =    -17

     -9    +    2    =    -7

     -6    +    3    =    -3    That's it

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

                    y2 - 6y + 3y - 18

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

                   y • (y-6)

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

                   3 • (y-6)

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

                   (y+3)  •  (y-6)

            Which is the desired factorization

Equation at the end of step

1

:

        10y      

 ————————————————— ÷ 5y ÷ (4y - 24)

 (y + 3) • (y - 6)

STEP

2

:

            10y          

Divide  ———————————  by  5y

        (y+3)•(y-6)      

Canceling Out :

2.1    Canceling out y as it appears on both sides of the fraction line

Equation at the end of step

2

:

         2        

 ————————————————— ÷ (4y - 24)

 (y + 3) • (y - 6)

STEP

3

:

             2          

Divide  ———————————  by  4y-24

        (y+3)•(y-6)      

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  4y - 24  =   4 • (y - 6)

Multiplying Exponential Expressions:

4.2    Multiply  (y - 6)  by  (y - 6)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (y-6)  and the exponents are :

         1 , as  (y-6)  is the same number as  (y-6)1

and   1 , as  (y-6)  is the same number as  (y-6)1

The product is therefore,  (y-6)(1+1) = (y-6)2

Final result :

            1          

 ——————————————————————

 2 • (y + 3) • (y - 6)2

true

explanation: