x(e^2x)-3=1

Solution for x(e^2x)-3=1 equation:

Simplifying
x(e2x) + -3 = 1

Multiply x * e2x
e2x2 + -3 = 1

Reorder the terms:
-3 + e2x2 = 1

Solving
-3 + e2x2 = 1

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + e2x2 = 1 + 3

Combine like terms: -3 + 3 = 0
0 + e2x2 = 1 + 3
e2x2 = 1 + 3

Combine like terms: 1 + 3 = 4
e2x2 = 4

Divide each side by 'x2'.
e2 = 4x-2

Simplifying
e2 = 4x-2

Take the square root of each side:
e = {-2x-1, 2x-1}