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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

4(4x-2)

We multiply parentheses

16x-8

Back to the equation:

-(16x-8)


We get rid of parentheses

2x^2+2x+4x-16x+4+8=0

We add all the numbers together, and all the variables

2x^2-10x+12=0

a = 2; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·2·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*2}=\frac{12}{4}
=3
$