4e+1=-4e^2

Solution for 4e+1=-4e^2 equation:

Simplifying
4e + 1 = -4e2

Reorder the terms:
1 + 4e = -4e2

Solving
1 + 4e = -4e2

Solving for variable 'e'.

Combine like terms: -4e2 + 4e2 = 0
1 + 4e + 4e2 = 0

Factor a trinomial.
(1 + 2e)(1 + 2e) = 0

Subproblem 1
Set the factor '(1 + 2e)' equal to zero and attempt to solve:

Simplifying
1 + 2e = 0

Solving
1 + 2e = 0

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

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

Combine like terms: 1 + -1 = 0
0 + 2e = 0 + -1
2e = 0 + -1

Combine like terms: 0 + -1 = -1
2e = -1

Divide each side by '2'.
e = -0.5

Simplifying
e = -0.5
Subproblem 2
Set the factor '(1 + 2e)' equal to zero and attempt to solve:

Simplifying
1 + 2e = 0

Solving
1 + 2e = 0

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

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

Combine like terms: 1 + -1 = 0
0 + 2e = 0 + -1
2e = 0 + -1

Combine like terms: 0 + -1 = -1
2e = -1

Divide each side by '2'.
e = -0.5

Simplifying
e = -0.5
Solution
e = {-0.5, -0.5}