(2x+4)(6x+3)=0

Solution for (2x+4)(6x+3)=0 equation:

(2x+4)(6x+3)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+30x+12=0

a = 12; b = 30; c = +12;
Δ = b2-4ac
Δ = 302-4·12·12
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*12}=\frac{-12}{24}
=-1/2
$