(3+z)(5z+7)=0

Solution for (3+z)(5z+7)=0 equation:

(3+z)(5z+7)=0

We add all the numbers together, and all the variables

(z+3)(5z+7)=0

We multiply parentheses ..

(+5z^2+7z+15z+21)=0

We get rid of parentheses

5z^2+7z+15z+21=0

We add all the numbers together, and all the variables

5z^2+22z+21=0

a = 5; b = 22; c = +21;
Δ = b2-4ac
Δ = 222-4·5·21
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-8}{2*5}=\frac{-30}{10}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+8}{2*5}=\frac{-14}{10}
=-1+2/5
$