SOLUTION: I am checking my work to the problem below: find all real solutions to the quadratic equation; 6p+2=p^2+3p^3 6p+2=p^2+3p^3 6p+2=3p^3+p^2 6p+2−(3p^3+p^2)=3p^3+p^2&#872

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I am checking my work to the problem below: find all real solutions to the quadratic equation; 6p+2=p^2+3p^3 6p+2=p^2+3p^3 6p+2=3p^3+p^2 6p+2−(3p^3+p^2)=3p^3+p^2&#872      Log On


   

Question 1037502: I am checking my work to the problem below:
find all real solutions to the quadratic equation; 6p+2=p^2+3p^3
6p+2=p^2+3p^3
6p+2=3p^3+p^2
6p+2−(3p^3+p^2)=3p^3+p^2−(3p^3+p^2)
−3p^3−p^2+6p+2=0
(−3p−1)(p^2−2)=0
−3p−1=0 or p^2−2=0
p= -1/3
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find all real solutions to the quadratic equation; 6p+2=p^2+3p^3
6p + 2 = p^2 + 3p^3
6p+2 = 3p^3 + p^2
************
3p^3 + p^2 - 6p - 2 = 0
p^2*(3p + 1) - 2*(3p + 1) = 0
(p^2 - 2)*(3p + 1) = 0
p = -1/3
=============
p^2 - 2 = 0
p = sqrt(2)
p = -sqrt(2)
*************************
6p+2 - (3p^3+p^2) = 3p^3 + p^2 - (3p^3+p^2)
-3p^3−p^2+6p+2=0
(−3p−1)(p^2−2)=0
−3p−1=0 or p^2−2=0
p= -1/3

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Rearrangement should be as 3p%5E3%2Bp%5E2-6p-2=0. Some other arrangement might allow easier factoring.

%28p%5E2%29%283p%2B1%29-%286p%2B2%29=0

%283p%2B1%29p%5E2-2%283p%2B1%29=0

%283p%2B1%29%28p%5E2-2%29=0

ZERO PRODUCT RULE
if 3p%2B1=0, then highlight%28p=-1%2F3%29.
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If p%5E2-2=0, then p%5E2=2, highlight%28p=-sqrt%282%29%29 or highlight%28p=sqrt%282%29%29.