(3x+6)(5x+4)=0

Solution for (3x+6)(5x+4)=0 equation:

(3x+6)(5x+4)=0

We multiply parentheses ..

(+15x^2+12x+30x+24)=0

We get rid of parentheses

15x^2+12x+30x+24=0

We add all the numbers together, and all the variables

15x^2+42x+24=0

a = 15; b = 42; c = +24;
Δ = b2-4ac
Δ = 422-4·15·24
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{-(42)-18}{2*15}=\frac{-60}{30}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+18}{2*15}=\frac{-24}{30}
=-4/5
$