e(2x)+2e(x)+1=0

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

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

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

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

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

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

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

Combine like terms: 2ex + 2ex = 4ex
1 + 4ex = 0

Solving
1 + 4ex = 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 + -1 + 4ex = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4ex = 0 + -1
4ex = 0 + -1

Combine like terms: 0 + -1 = -1
4ex = -1

Divide each side by '4x'.
e = -0.25x-1

Simplifying
e = -0.25x-1