(-2x+2)(x+4)-(-5x-5)(x+1)=2(x+1)(x+4)

Solution for (-2x+2)(x+4)-(-5x-5)(x+1)=2(x+1)(x+4) equation:

(-2x+2)(x+4)-(-5x-5)(x+1)=2(x+1)(x+4)

We move all terms to the left:

(-2x+2)(x+4)-(-5x-5)(x+1)-(2(x+1)(x+4))=0

We multiply parentheses ..

(-2x^2-8x+2x+8)-(-5x-5)(x+1)-(2(x+1)(x+4))=0


We calculate terms in parentheses: -(2(x+1)(x+4)), so:

2(x+1)(x+4)

We multiply parentheses ..

2(+x^2+4x+x+4)

We multiply parentheses

2x^2+8x+2x+8

We add all the numbers together, and all the variables

2x^2+10x+8

Back to the equation:

-(2x^2+10x+8)


We get rid of parentheses

-2x^2-2x^2-8x+2x-(-5x-5)(x+1)-10x+8-8=0

We multiply parentheses ..

-2x^2-2x^2-(-5x^2-5x-5x-5)-8x+2x-10x+8-8=0

We add all the numbers together, and all the variables

-4x^2-(-5x^2-5x-5x-5)-16x=0

We get rid of parentheses

-4x^2+5x^2+5x+5x-16x+5=0

We add all the numbers together, and all the variables

x^2-6x+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$