(p+3)(2p-2)=4p+3

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

(p+3)(2p-2)=4p+3

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

2p^2-2p+6p-4p-6-3=0

We add all the numbers together, and all the variables

2p^2-9=0

a = 2; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·2·(-9)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*2}=\frac{0-6\sqrt{2}}{4}
=-\frac{6\sqrt{2}}{4}
=-\frac{3\sqrt{2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*2}=\frac{0+6\sqrt{2}}{4}
=\frac{6\sqrt{2}}{4}
=\frac{3\sqrt{2}}{2}
$