(u+6)(u+1)=-6

Solution for (u+6)(u+1)=-6 equation:

(u+6)(u+1)=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

(u+6)(u+1)+6=0

We multiply parentheses ..

(+u^2+u+6u+6)+6=0

We get rid of parentheses

u^2+u+6u+6+6=0

We add all the numbers together, and all the variables

u^2+7u+12=0

a = 1; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·1·12
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*1}=\frac{-8}{2}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*1}=\frac{-6}{2}
=-3
$