(3a-2)(5a-4)=(3a-2)

Solution for (3a-2)(5a-4)=(3a-2) equation:

(3a-2)(5a-4)=(3a-2)

We move all terms to the left:

(3a-2)(5a-4)-((3a-2))=0

We multiply parentheses ..

(+15a^2-12a-10a+8)-((3a-2))=0


We calculate terms in parentheses: -((3a-2)), so:

(3a-2)

We get rid of parentheses

3a-2

Back to the equation:

-(3a-2)


We get rid of parentheses

15a^2-12a-10a-3a+8+2=0

We add all the numbers together, and all the variables

15a^2-25a+10=0

a = 15; b = -25; c = +10;
Δ = b2-4ac
Δ = -252-4·15·10
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5}{2*15}=\frac{20}{30}
=2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*15}=\frac{30}{30}
=1
$