(3x+6)(2-x)-(3x+6)(-4x+3)=0

Solution for (3x+6)(2-x)-(3x+6)(-4x+3)=0 equation:

(3x+6)(2-x)-(3x+6)(-4x+3)=0

We add all the numbers together, and all the variables

(3x+6)(-1x+2)-(3x+6)(-4x+3)=0

We multiply parentheses ..

(-3x^2+6x-6x+12)-(3x+6)(-4x+3)=0

We get rid of parentheses

-3x^2+6x-6x-(3x+6)(-4x+3)+12=0

We multiply parentheses ..

-3x^2-(-12x^2+9x-24x+18)+6x-6x+12=0

We add all the numbers together, and all the variables

-3x^2-(-12x^2+9x-24x+18)+12=0

We get rid of parentheses

-3x^2+12x^2-9x+24x-18+12=0

We add all the numbers together, and all the variables

9x^2+15x-6=0

a = 9; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·9·(-6)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*9}=\frac{-36}{18}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*9}=\frac{6}{18}
=1/3
$