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

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

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

We add all the numbers together, and all the variables

4(-1x+6)(x+3)=0

We multiply parentheses ..

4(-1x^2-3x+6x+18)=0

We multiply parentheses

-4x^2-12x+24x+72=0

We add all the numbers together, and all the variables

-4x^2+12x+72=0

a = -4; b = 12; c = +72;
Δ = b2-4ac
Δ = 122-4·(-4)·72
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*-4}=\frac{24}{-8}
=-3
$