(6p+3)(6p-7)-(7p-4)(-p-2)=0

Solution for (6p+3)(6p-7)-(7p-4)(-p-2)=0 equation:

(6p+3)(6p-7)-(7p-4)(-p-2)=0

We add all the numbers together, and all the variables

(6p+3)(6p-7)-(7p-4)(-1p-2)=0

We multiply parentheses ..

(+36p^2-42p+18p-21)-(7p-4)(-1p-2)=0

We get rid of parentheses

36p^2-42p+18p-(7p-4)(-1p-2)-21=0

We multiply parentheses ..

36p^2-(-7p^2-14p+4p+8)-42p+18p-21=0

We add all the numbers together, and all the variables

36p^2-(-7p^2-14p+4p+8)-24p-21=0

We get rid of parentheses

36p^2+7p^2+14p-4p-24p-8-21=0

We add all the numbers together, and all the variables

43p^2-14p-29=0

a = 43; b = -14; c = -29;
Δ = b2-4ac
Δ = -142-4·43·(-29)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-72}{2*43}=\frac{-58}{86}
=-29/43
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+72}{2*43}=\frac{86}{86}
=1
$