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

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

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

We multiply parentheses ..

(+3x^2-9x+12x-36)=0

We get rid of parentheses

3x^2-9x+12x-36=0

We add all the numbers together, and all the variables

3x^2+3x-36=0

a = 3; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·3·(-36)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*3}=\frac{18}{6}
=3
$