Why was all the negatives turned to positives?

Question

2x2 + 5(x + 3) - 4x2 - 12x = 18
2x2 + 5x + 15 - 4x2 - 12x = 18
-2x2 -7x - 3 = 0
2x2 + 7x + 3 = 0
Simplify each fractional expression and then write the equation in standard quadratic form.

Answer 1

Not sure I really understand your question, "why did the negatives turn to positives," but here is my interpretation.  I assume you are asking how -2x2-7x-3 was converted to 2x2+7x+3; two ways, multiply both sides by -1 (minus one) ... -1 * 0 = 0 ... or, add 2x2+7x+3 to both sides.

 

on to the final solution, I.e., by factoring you get

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

so, x =-1/2 or x= -3

 

Was this what you were asking?

 

Answer 2

Looks like this 2x2 + 5(x + 3) - 4x2 - 12x = 18

 

should be this 2x^2 + 5(x + 3) - 4x^2 - 12x = 18; then:

 

2x^2 - 4x^2 + 5x + 15 - 12x = 18

                    -12x -  18 +12x = -18

-2x^2           - 7x  -   3          =  0

 

Multiply both sides by -1:

 

2x^2 + 7x + 3 = 0