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

Solution for 4(x-3)(x+1)=0 equation:

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

We multiply parentheses ..

4(+x^2+x-3x-3)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

4x^2-8x-12=0

a = 4; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·4·(-12)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*4}=\frac{24}{8}
=3
$