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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(x+2)(x+4)

We multiply parentheses ..

(+x^2+4x+2x+8)

We get rid of parentheses

x^2+4x+2x+8

We add all the numbers together, and all the variables

x^2+6x+8

Back to the equation:

-(x^2+6x+8)


We get rid of parentheses

2x^2-x^2+4x+2x-6x+4-8=0

We add all the numbers together, and all the variables

x^2-4=0

a = 1; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1·(-4)
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{-(0)-4}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*1}=\frac{4}{2}
=2
$