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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

-4x^2-12x+2x+6-6=0

We add all the numbers together, and all the variables

-4x^2-10x=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$