Answer:3a2+17a+10=0

Two solutions were found :

a = -5

a = -2/3 = -0.667

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a2" was replaced by "a^2".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(3a2 + 17a) + 10 = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 3a2+17a+10

The first term is, 3a2 its coefficient is 3 .

The middle term is, +17a its coefficient is 17 .

The last term, "the constant", is +10

Step-1 : Multiply the coefficient of the first term by the constant 3 • 10 = 30

Step-2 : Find two factors of 30 whose sum equals the coefficient of the middle term, which is 17 .

-30 + -1 = -31

-15 + -2 = -17

-10 + -3 = -13

-6 + -5 = -11

-5 + -6 = -11

-3 + -10 = -13

-2 + -15 = -17

-1 + -30 = -31

1 + 30 = 31

2 + 15 = 17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 15

3a2 + 2a + 15a + 10

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

a • (3a+2)

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

5 • (3a+2)

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

(a+5) • (3a+2)

Which is the desired factorization

Equation at the end of step 2 :

(3a + 2) • (a + 5) = 0

3a+2=0

3a=-2

a=-2/3

a+5=0

a=-5

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Step-by-step explanation: