2x+12=2x(x+6)

Solution for 2x+12=2x(x+6) equation:

2x+12=2x(x+6)

We move all terms to the left:

2x+12-(2x(x+6))=0


We calculate terms in parentheses: -(2x(x+6)), so:

2x(x+6)

We multiply parentheses

2x^2+12x

Back to the equation:

-(2x^2+12x)


We get rid of parentheses

-2x^2+2x-12x+12=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 = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-2}=\frac{24}{-4}
=-6
$