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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-4u^2+36u-72=0

a = -4; b = 36; c = -72;
Δ = b2-4ac
Δ = 362-4·(-4)·(-72)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12}{2*-4}=\frac{-48}{-8}
=+6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12}{2*-4}=\frac{-24}{-8}
=+3
$