p=(2p-6)(p+1)

Solution for p=(2p-6)(p+1) equation:

p=(2p-6)(p+1)

We move all terms to the left:

p-((2p-6)(p+1))=0

We multiply parentheses ..

-((+2p^2+2p-6p-6))+p=0


We calculate terms in parentheses: -((+2p^2+2p-6p-6)), so:

(+2p^2+2p-6p-6)

We get rid of parentheses

2p^2+2p-6p-6

We add all the numbers together, and all the variables

2p^2-4p-6

Back to the equation:

-(2p^2-4p-6)


We add all the numbers together, and all the variables

p-(2p^2-4p-6)=0

We get rid of parentheses

-2p^2+p+4p+6=0

We add all the numbers together, and all the variables

-2p^2+5p+6=0

a = -2; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-2)·6
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{73}}{2*-2}=\frac{-5-\sqrt{73}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-2}=\frac{-5+\sqrt{73}}{-4}
$