6x(3x+2)=5(3x+2)=0

Solution for 6x(3x+2)=5(3x+2)=0 equation:

6x(3x+2)=5(3x+2)=0

We move all terms to the left:

6x(3x+2)-(5(3x+2))=0

We multiply parentheses

18x^2+12x-(5(3x+2))=0


We calculate terms in parentheses: -(5(3x+2)), so:

5(3x+2)

We multiply parentheses

15x+10

Back to the equation:

-(15x+10)


We get rid of parentheses

18x^2+12x-15x-10=0

We add all the numbers together, and all the variables

18x^2-3x-10=0

a = 18; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·18·(-10)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*18}=\frac{-24}{36}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*18}=\frac{30}{36}
=5/6
$