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

Solution for (-2x+1)(x+4)+2(2x+-1)(x+1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2-8x+x+4)+2(2x-1)(x+1)=0

We get rid of parentheses

-2x^2-8x+x+2(2x-1)(x+1)+4=0

We multiply parentheses ..

-2x^2+2(+2x^2+2x-1x-1)-8x+x+4=0

We add all the numbers together, and all the variables

-2x^2+2(+2x^2+2x-1x-1)-7x+4=0

We multiply parentheses

-2x^2+4x^2+4x-2x-7x-2+4=0

We add all the numbers together, and all the variables

2x^2-5x+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$