(p-7)(p-12)+(2p+9)(p+11)=p(2p+14)+207

Solution for (p-7)(p-12)+(2p+9)(p+11)=p(2p+14)+207 equation:

(p-7)(p-12)+(2p+9)(p+11)=p(2p+14)+207

We move all terms to the left:

(p-7)(p-12)+(2p+9)(p+11)-(p(2p+14)+207)=0

We multiply parentheses ..

(+p^2-12p-7p+84)+(2p+9)(p+11)-(p(2p+14)+207)=0


We calculate terms in parentheses: -(p(2p+14)+207), so:

p(2p+14)+207

We multiply parentheses

2p^2+14p+207

Back to the equation:

-(2p^2+14p+207)


We get rid of parentheses

p^2-2p^2-12p-7p+(2p+9)(p+11)-14p+84-207=0

We multiply parentheses ..

p^2-2p^2+(+2p^2+22p+9p+99)-12p-7p-14p+84-207=0

We add all the numbers together, and all the variables

-1p^2+(+2p^2+22p+9p+99)-33p-123=0

We get rid of parentheses

-1p^2+2p^2+22p+9p-33p+99-123=0

We add all the numbers together, and all the variables

p^2-2p-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$