(-5p+8)(3p+2)=0

Solution for (-5p+8)(3p+2)=0 equation:

(-5p+8)(3p+2)=0

We multiply parentheses ..

(-15p^2-10p+24p+16)=0

We get rid of parentheses

-15p^2-10p+24p+16=0

We add all the numbers together, and all the variables

-15p^2+14p+16=0

a = -15; b = 14; c = +16;
Δ = b2-4ac
Δ = 142-4·(-15)·16
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*-15}=\frac{-48}{-30}
=1+3/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*-15}=\frac{20}{-30}
=-2/3
$