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# Why was all the negatives turned to positives?

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.

Yes, thank you. That was the question. An additional question: Is there a rule that says multiply by -1? How would I knowknow when to do that?
You do NOT "need" to multiply by -1.  It just makes it easier to deal with positive coefficients, rather than negative one.  BUT, PRINCIPALLY, THE STATEMENT(S) "MULTIPLY BY -1" ADDRESS YOUR ORIGINAL QUESTION, "why was all the negatives turned to positives"?  You get the same positive coefficient result by adding 2x2+7x+3 to both sides ... It is the equivalent of 'multiply by -1'"

There is no rule, just a matter of convenience.

### 2 Answers by Expert Tutors

Alex S. | Retired, Looking to Share My Love of Mathematics and ComputersRetired, Looking to Share My Love of Mat...
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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

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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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