(3x+12)(4x+2)=0

Solution for (3x+12)(4x+2)=0 equation:

(3x+12)(4x+2)=0

We multiply parentheses ..

(+12x^2+6x+48x+24)=0

We get rid of parentheses

12x^2+6x+48x+24=0

We add all the numbers together, and all the variables

12x^2+54x+24=0

a = 12; b = 54; c = +24;
Δ = b2-4ac
Δ = 542-4·12·24
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-42}{2*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+42}{2*12}=\frac{-12}{24}
=-1/2
$