(4x+12)(x+5)=0

Solution for (4x+12)(x+5)=0 equation:

(4x+12)(x+5)=0

We multiply parentheses ..

(+4x^2+20x+12x+60)=0

We get rid of parentheses

4x^2+20x+12x+60=0

We add all the numbers together, and all the variables

4x^2+32x+60=0

a = 4; b = 32; c = +60;
Δ = b2-4ac
Δ = 322-4·4·60
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8}{2*4}=\frac{-24}{8}
=-3
$