(X+5)(3x-1)+(x+5)(2x+1)=0

Solution for (X+5)(3x-1)+(x+5)(2x+1)=0 equation:

(X+5)(3X-1)+(X+5)(2X+1)=0

We multiply parentheses ..

(+3X^2-1X+15X-5)+(X+5)(2X+1)=0

We get rid of parentheses

3X^2-1X+15X+(X+5)(2X+1)-5=0

We multiply parentheses ..

3X^2+(+2X^2+X+10X+5)-1X+15X-5=0

We add all the numbers together, and all the variables

3X^2+(+2X^2+X+10X+5)+14X-5=0

We get rid of parentheses

3X^2+2X^2+X+10X+14X+5-5=0

We add all the numbers together, and all the variables

5X^2+25X=0

a = 5; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·5·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*5}=\frac{-50}{10}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*5}=\frac{0}{10}
=0
$