(2z+7)(2+z)=0

Solution for (2z+7)(2+z)=0 equation:

(2z+7)(2+z)=0

We add all the numbers together, and all the variables

(2z+7)(z+2)=0

We multiply parentheses ..

(+2z^2+4z+7z+14)=0

We get rid of parentheses

2z^2+4z+7z+14=0

We add all the numbers together, and all the variables

2z^2+11z+14=0

a = 2; b = 11; c = +14;
Δ = b2-4ac
Δ = 112-4·2·14
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3}{2*2}=\frac{-14}{4}
=-3+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*2}=\frac{-8}{4}
=-2
$