z^2+27z=0

Solution for z^2+27z=0 equation:

Simplifying
z2 + 27z = 0

Reorder the terms:
27z + z2 = 0

Solving
27z + z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(27 + z) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(27 + z)' equal to zero and attempt to solve:

Simplifying
27 + z = 0

Solving
27 + z = 0

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

Add '-27' to each side of the equation.
27 + -27 + z = 0 + -27

Combine like terms: 27 + -27 = 0
0 + z = 0 + -27
z = 0 + -27

Combine like terms: 0 + -27 = -27
z = -27

Simplifying
z = -27
Solution
z = {0, -27}