(x-10)(2x+2)+(x-10)(x+1)=0

Solution for (x-10)(2x+2)+(x-10)(x+1)=0 equation:

(x-10)(2x+2)+(x-10)(x+1)=0

We multiply parentheses ..

(+2x^2+2x-20x-20)+(x-10)(x+1)=0

We get rid of parentheses

2x^2+2x-20x+(x-10)(x+1)-20=0

We multiply parentheses ..

2x^2+(+x^2+x-10x-10)+2x-20x-20=0

We add all the numbers together, and all the variables

2x^2+(+x^2+x-10x-10)-18x-20=0

We get rid of parentheses

2x^2+x^2+x-10x-18x-10-20=0

We add all the numbers together, and all the variables

3x^2-27x-30=0

a = 3; b = -27; c = -30;
Δ = b2-4ac
Δ = -272-4·3·(-30)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*3}=\frac{60}{6}
=10
$