(x+4)*(x+2)=2*(x+10)

Solution for (x+4)*(x+2)=2*(x+10) equation:

(x+4)(x+2)=2(x+10)

We move all terms to the left:

(x+4)(x+2)-(2(x+10))=0

We multiply parentheses ..

(+x^2+2x+4x+8)-(2(x+10))=0


We calculate terms in parentheses: -(2(x+10)), so:

2(x+10)

We multiply parentheses

2x+20

Back to the equation:

-(2x+20)


We get rid of parentheses

x^2+2x+4x-2x+8-20=0

We add all the numbers together, and all the variables

x^2+4x-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$