(5p+2)(2p-3)=0

Solution for (5p+2)(2p-3)=0 equation:

(5p+2)(2p-3)=0

We multiply parentheses ..

(+10p^2-15p+4p-6)=0

We get rid of parentheses

10p^2-15p+4p-6=0

We add all the numbers together, and all the variables

10p^2-11p-6=0

a = 10; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·10·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*10}=\frac{-8}{20}
=-2/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*10}=\frac{30}{20}
=1+1/2
$