Question 12636
You need to get Zero on the right side of the equation by subtracting 6p and 5 from both sides of your equation, this leaves you with...

{{{ p^2 + 9p + 20 = 0 }}}
Now you need to find the roots,
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Step 1: Multiply the P^2 Coefficient with your constant ( 1 * 20 ) = 20
Step 2: List the factors of 20
<LI> 20, 1
<LI> 10, 2
<LI> 5, 4
<LI> -4, -5
<LI> -2, -10
<LI> -1, -20
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Step 3: Out of the factors, are there any that when you add them together give you your P term, in this case 9. 
<LI> Yes ( 5 + 4 = 9 )
Step 4: Split the middle term into its two factors
<LI> {{{ P^2 + 5P + 4P + 20 = 0}}} <--- Unfoil
Step 5: Group
<LI> {{{ (P^2 + 5P) + (4P + 20)= 0 }}}
Step 6: Take out GCF From each group
<LI> {{{ P(P + 5) + 4(P + 5) = 0}}}
Step 7: You need two sets of '()' one set is the one term inside '()' the other set is what is left over ( technically factoring out a (P+5) )
<LI> {{{ (P + 5)(P + 4) = 0}}}
Step 8: FOIL to Check
Step 9: the ROOTS of a Quadratic are where the Quadratic crosses the X-Axis, and where the function evaluates to Zero.
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In order for {{{ (P + 5)(P + 4) = 0 }}} to be true either
<LI> P + 5 = 0 There for P = -5 OR
<LI> P + 4 = 0 There for P = -4

So, -5 and -4 are your roots