(5-2y)(2+3y)=0

Solution for (5-2y)(2+3y)=0 equation:

(5-2y)(2+3y)=0

We add all the numbers together, and all the variables

(-2y+5)(3y+2)=0

We multiply parentheses ..

(-6y^2-4y+15y+10)=0

We get rid of parentheses

-6y^2-4y+15y+10=0

We add all the numbers together, and all the variables

-6y^2+11y+10=0

a = -6; b = 11; c = +10;
Δ = b2-4ac
Δ = 112-4·(-6)·10
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*-6}=\frac{8}{-12}
=-2/3
$