E=2E(4+E)-E

Solution for E=2E(4+E)-E equation:

Simplifying
E = 2E(4 + E) + -1E
E = (4 * 2E + E * 2E) + -1E
E = (8E + 2E2) + -1E

Reorder the terms:
E = 8E + -1E + 2E2

Combine like terms: 8E + -1E = 7E
E = 7E + 2E2

Solving
E = 7E + 2E2

Solving for variable 'E'.

Combine like terms: E + -7E = -6E
-6E + -2E2 = 7E + 2E2 + -7E + -2E2

Reorder the terms:
-6E + -2E2 = 7E + -7E + 2E2 + -2E2

Combine like terms: 7E + -7E = 0
-6E + -2E2 = 0 + 2E2 + -2E2
-6E + -2E2 = 2E2 + -2E2

Combine like terms: 2E2 + -2E2 = 0
-6E + -2E2 = 0

Factor out the Greatest Common Factor (GCF), '-2E'.
-2E(3 + E) = 0

Ignore the factor -2.
Subproblem 1
Set the factor 'E' equal to zero and attempt to solve:

Simplifying
E = 0

Solving
E = 0

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

Simplifying
E = 0
Subproblem 2
Set the factor '(3 + E)' equal to zero and attempt to solve:

Simplifying
3 + E = 0

Solving
3 + E = 0

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

Add '-3' to each side of the equation.
3 + -3 + E = 0 + -3

Combine like terms: 3 + -3 = 0
0 + E = 0 + -3
E = 0 + -3

Combine like terms: 0 + -3 = -3
E = -3

Simplifying
E = -3
Solution
E = {0, -3}