Question

Solve (x+2)(2x+3)=6
{-2,3/2}
{-7/2,0}
{0}

Answer 1

To solve the equation (x+2)(2x+3)=6, expand, simplify, and factor to find the values of x.

Step-by-step explanation:

To solve the equation (x+2)(2x+3)=6, we can expand it and then simplify it.

x^2+7x+6=6

x^2+7x=0

Now we can factor out the common factor x and solve for x:

x(x+7)=0

So, the two possible values of x are -7 and 0.

Answer 2

{-7/2,0}

Step-by-step explanation:

(x+2)(2x+3)=6

FOIL

first 2x^2

outer 3x

inner 4x

last 6

2x^2 +7x+6

2x^2 +7x+6 = 6

Subtract 6 from each side

2x^2 +7x+6-6 = 6-6

2x^2 +7x =0

Factor out x

x(2x+7) =0

Using the zero product property

x=0 2x+7 =0

x=0 2x=-7

x=0 x = -7/2