(30+3x)(12-2x)=0

Solution for (30+3x)(12-2x)=0 equation:

(30+3x)(12-2x)=0

We add all the numbers together, and all the variables

(3x+30)(-2x+12)=0

We multiply parentheses ..

(-6x^2+36x-60x+360)=0

We get rid of parentheses

-6x^2+36x-60x+360=0

We add all the numbers together, and all the variables

-6x^2-24x+360=0

a = -6; b = -24; c = +360;
Δ = b2-4ac
Δ = -242-4·(-6)·360
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-96}{2*-6}=\frac{-72}{-12}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+96}{2*-6}=\frac{120}{-12}
=-10
$