z^2+34z=0

Solution for z^2+34z=0 equation:

Simplifying
z2 + 34z = 0

Reorder the terms:
34z + z2 = 0

Solving
34z + z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(34 + 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 '(34 + z)' equal to zero and attempt to solve:

Simplifying
34 + z = 0

Solving
34 + z = 0

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

Add '-34' to each side of the equation.
34 + -34 + z = 0 + -34

Combine like terms: 34 + -34 = 0
0 + z = 0 + -34
z = 0 + -34

Combine like terms: 0 + -34 = -34
z = -34

Simplifying
z = -34
Solution
z = {0, -34}