e(2x)-2e(x)*x-1=0

Solution for e(2x)-2e(x)*x-1=0 equation:

Simplifying
e(2x) + -2e(x) * x + -1 = 0

Remove parenthesis around (2x)
e * 2x + -2e(x) * x + -1 = 0

Reorder the terms for easier multiplication:
2e * x + -2e(x) * x + -1 = 0

Multiply e * x
2ex + -2e(x) * x + -1 = 0

Multiply e * x
2ex + -2ex * x + -1 = 0

Multiply ex * x
2ex + -2ex2 + -1 = 0

Reorder the terms:
-1 + 2ex + -2ex2 = 0

Solving
-1 + 2ex + -2ex2 = 0

Solving for variable 'e'.

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

Add '1' to each side of the equation.
-1 + 2ex + 1 + -2ex2 = 0 + 1

Reorder the terms:
-1 + 1 + 2ex + -2ex2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2ex + -2ex2 = 0 + 1
2ex + -2ex2 = 0 + 1

Combine like terms: 0 + 1 = 1
2ex + -2ex2 = 1

Reorder the terms:
-1 + 2ex + -2ex2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2ex + -2ex2 = 0

The solution to this equation could not be determined.