(3z-1)(3+z)=0

Solution for (3z-1)(3+z)=0 equation:

(3z-1)(3+z)=0

We add all the numbers together, and all the variables

(3z-1)(z+3)=0

We multiply parentheses ..

(+3z^2+9z-1z-3)=0

We get rid of parentheses

3z^2+9z-1z-3=0

We add all the numbers together, and all the variables

3z^2+8z-3=0

a = 3; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·3·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*3}=\frac{-18}{6}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*3}=\frac{2}{6}
=1/3
$