(5p+3)(8p+7)=0

Solution for (5p+3)(8p+7)=0 equation:

(5p+3)(8p+7)=0

We multiply parentheses ..

(+40p^2+35p+24p+21)=0

We get rid of parentheses

40p^2+35p+24p+21=0

We add all the numbers together, and all the variables

40p^2+59p+21=0

a = 40; b = 59; c = +21;
Δ = b2-4ac
Δ = 592-4·40·21
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-11}{2*40}=\frac{-70}{80}
=-7/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+11}{2*40}=\frac{-48}{80}
=-3/5
$