What times what equals -72 but adds to get -34? Solve the equation by factoring- 3x^2-34x-24=0

First part:
-36 * 2 = -72
-36 + 2 = -34
Second part: Assuming that the 3x^2 is positive. (the answers are bolded)
3x^2-34x-24=0
(x-12)(3x+2)=0
x-12=0             3x+2=0
 +12  +12             -2   -2
x=12                 3x=-2
                         \( \frac{3x}{3}= \frac{-2}{3} \)
                         x=\( \frac{-2}{3} \)

OK SO THE THING WE HAVE TO FACTOR DOESN"T RELATE TO THE PROBLEM
easy way to solve is factor -72 and find what factos add up so 34
-72=
1,72=-71 no
2,36=-34 correct
therefor the numbers are 2 and -36
that was easy
now the legit math way
so
xy=-72
x+y=-34
x+y=-34
subtract x
y=-34-x
subsitute
x(-34-x)=-72
-34x-x^2=-72
add 34x+x^2 to bboth sides
0=x^2+34x-72
factor
facotr -72 and find what 2 factors add up to 34
-2 and 36 add up to 34
(x-2)(x+36)=0
set each to zero
x-2=0
add 2
x=2
 
x+36=0
subtract 36
x=-36
the numbers are 2 and -36
Second question
factor 3x^2-34x-24 which has nothing to do with the problem except ahthat 3 times 24=72
 we do is we factor the first term
3=1 times 3
we know that it will be in a form liike
(somethingx+something)(somethingx+something) so
we put the 1 and 3 for the first somethings
(3x+ something)(1x+something)
then we factor 24
24=1 and 24 or 2 and 12 or 3 and 8 or 4 and 6
let’s pick a random pair
2 and 12
they have to be different signs  since the last term is negative
since midlde term is also negative, we know that bigge number is negative so
(3x+2)(x-12)
we expand
3x^2+2x-36x-24
3x^2-34x-24
ok, so I don’t know what the equiqation was for but
numbers are 2 and -36
facotre form of equation that didn’t relate=(3x+2)(x-12)

what’s funny is that the equation doesn’ help solve the question about what 2 numbers multipyto -72 andadd to -34


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