-4t(t+6)=0

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

-4t(t+6)=0

We multiply parentheses

-4t^2-24t=0

a = -4; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-4)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-4}=\frac{0}{-8}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-4}=\frac{48}{-8}
=-6
$