(3m-2)(9m-5)=0

Solution for (3m-2)(9m-5)=0 equation:

(3m-2)(9m-5)=0

We multiply parentheses ..

(+27m^2-15m-18m+10)=0

We get rid of parentheses

27m^2-15m-18m+10=0

We add all the numbers together, and all the variables

27m^2-33m+10=0

a = 27; b = -33; c = +10;
Δ = b2-4ac
Δ = -332-4·27·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*27}=\frac{30}{54}
=5/9
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*27}=\frac{36}{54}
=2/3
$