a^2+14a=0

Solution for a^2+14a=0 equation:

Simplifying
a2 + 14a = 0

Reorder the terms:
14a + a2 = 0

Solving
14a + a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(14 + a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(14 + a)' equal to zero and attempt to solve:

Simplifying
14 + a = 0

Solving
14 + a = 0

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

Add '-14' to each side of the equation.
14 + -14 + a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + a = 0 + -14
a = 0 + -14

Combine like terms: 0 + -14 = -14
a = -14

Simplifying
a = -14
Solution
a = {0, -14}