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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-4u^2-12u+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:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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