algebra 2 ?

2 (x2 + 7x + 3) 

= 4x2 + 14x + 6

= 4x2 + 14x + 6 - 6 = 0 - 6

= 4x2 + 14x =  (-6)

= 4x2 + 14x  = - 6

    -----------

         2

Final result would be: 

 2x2 + 7x  = -6

It's a quadratic, so try the quadratic formula:

x = (-7 +/- sqrt(7^2 - 4*2*3))/(2*2) = (-7 +/-sqrt(49 - 24))/4 = (-7 +/- 5)/4 = -3 or -1/2so (2x+1)(x+3)or.... 2 = 2*1 and 3 = 3* 17 = 2*3 + 1*1so (2x+1)(x+3)or==> (2x^2 + x) + (6x + 3)==> x(2x+1) + 3(2x+1)==> (2x+1)(x+3)

2x^2 + 7x + 3

Factors to

( 2x + 1)(x + 3

2x^2 + 7x + 3 

Factors to 

( 2x + 1)(x + 3) 

2x^2 + 7x + 3

= 2x^2 + 6x + x + 3

= 2x(x + 3) + (x + 3)

= (2x + 1)(x + 3)

Break up the middle term into two terms, i.e. find two numbers with a sum of 7 and a product of 2*3=6. So they must be 1 and 6. So we have:

= 2x^2 + x + 6x + 3

Find a common factor for the first two terms, and find a common factor for the next two terms:

= x(2x + 1) + 3(2x + 1)

Now factor using (2x + 1) as a common factor:

= (x + 3)(2x + 1)

If the above doesn't work, first find the roots using the quadratic formula:

x = (-7 +/- sqrt(7^2 - 4*2*3)) / (2*2)

x = (-7 +/- sqrt(49 - 24)) / 4

x = (-7 +/- sqrt(25)) / 4

x = (-7 +/- 5) / 4

x = (-12 or -2) / 4

x = -3 or -0.5

So the original expression must be some multiple of:

(x + 3)(x + 0.5) which is the same as x^2 + 3.5x + 1.5

We need to multiply that by 2 to get back to the original expression.

So we have 2(x + 3)(x + 0.5), which is the same as (x + 3)(2x + 1)

(2x+5)(x+1)=2x²+5x+2x+5=2x²+7x+5

So 2x²+7x+3=-2

2x^2+7x+3=(2x+1)(x+3)