(2+3x)(4x)-3x(3-x)=0

Solution for (2+3x)(4x)-3x(3-x)=0 equation:

(2+3x)(4x)-3x(3-x)=0

We add all the numbers together, and all the variables

(3x+2)4x-3x(-1x+3)=0

We multiply parentheses

12x^2+3x^2+8x-9x=0

We add all the numbers together, and all the variables

15x^2-1x=0

a = 15; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·15·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*15}=\frac{2}{30}
=1/15
$