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

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

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

We multiply parentheses ..

2(+x^2+2x+3x+6)=0

We multiply parentheses

2x^2+4x+6x+12=0

We add all the numbers together, and all the variables

2x^2+10x+12=0

a = 2; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·2·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*2}=\frac{-8}{4}
=-2
$