Question

`2x^2+5x+3=0`

Show Work!

Solve by factoring, please!

Answer 1

`x=-(3)/(2),-1`

Explanation:

`2x^2+5x+3=0`

Split the second term (5x) into two terms. Multiply the coefficient of the first term (2) by the constant term (3):

`2*3=6`

Find which two numbers add up to 5 and multiply into 6:

`3+2=5\\3*2=6\\3,2`

Split 5x as the sum of 3x and 2x:

`2x^2+3x+2x+3`

Now factor out a common term for the first 2 terms:

`2x^2+3x\\x(2x+3)`

And do the same for the last 2 terms:

`2x+3\\1(2x+3)`

Re-insert:

`x(2x+3)+1(2x+3)=0`

Factor out the common term 2x+3 and insert the values in front of the parentheses (x and 1):

`(2x+3)(x+1)=0`

Separate the parentheses and equal them to 0. Solve for x:

`2x+3=0\\2x+3-3=0-3\\2x=-3\\\\(2x)/(2)=(-3)/(2)\\\\ x=-(3)/(2)`

and

`x+1=0\\x+1-1=0-1\\x=-1`