Find x for the identity is true 1+12^6x = 2*12^3x

This is an exponential equation that
requires substitution technique.

First,
we'll move all terms to one side, changing the sign of the terms
moved.

12^6x - 2*12^3x + 1 =
0

It is a bi-quadratic
equation:

We'll substitute 12^3x  by another
variable.

12^3x  = t

We'll
square raise both sides:

12^6x  =
t^2

 We'll re-write the equtaion, having "t" as
variable.

t^2 - 2t + 1 = 0

The
equation above is the result of expanding the
square:

(t-1)^2 = 0

t1 = t2 =
1

But 12^3x = t1.

12^3x =
1

We'll write 1 as a power of
12:

12^3x= 12^0

Since the
bases are matching, we'll apply the one to one property:

3x
= 0

We'll divide by 3 both
sides:

x =
0.

The solution of the equation is x =
0.