(e+6)(2e+6)=0

Solution for (e+6)(2e+6)=0 equation:

Simplifying
(e + 6)(2e + 6) = 0

Reorder the terms:
(6 + e)(2e + 6) = 0

Reorder the terms:
(6 + e)(6 + 2e) = 0

Multiply (6 + e) * (6 + 2e)
(6(6 + 2e) + e(6 + 2e)) = 0
((6 * 6 + 2e * 6) + e(6 + 2e)) = 0
((36 + 12e) + e(6 + 2e)) = 0
(36 + 12e + (6 * e + 2e * e)) = 0
(36 + 12e + (6e + 2e2)) = 0

Combine like terms: 12e + 6e = 18e
(36 + 18e + 2e2) = 0

Solving
36 + 18e + 2e2 = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 9e + e2) = 0

Factor a trinomial.
2((6 + e)(3 + e)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + e)' equal to zero and attempt to solve:

Simplifying
6 + e = 0

Solving
6 + e = 0

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

Add '-6' to each side of the equation.
6 + -6 + e = 0 + -6

Combine like terms: 6 + -6 = 0
0 + e = 0 + -6
e = 0 + -6

Combine like terms: 0 + -6 = -6
e = -6

Simplifying
e = -6
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 = {-6, -3}