-42z^2=z

Solution for -42z^2=z equation:

Simplifying
-42z2 = z

Solving
-42z2 = z

Solving for variable 'z'.

Reorder the terms:
-1z + -42z2 = z + -1z

Combine like terms: z + -1z = 0
-1z + -42z2 = 0

Factor out the Greatest Common Factor (GCF), '-1z'.
-1z(1 + 42z) = 0

Ignore the factor -1.
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 '(1 + 42z)' equal to zero and attempt to solve:

Simplifying
1 + 42z = 0

Solving
1 + 42z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 42z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 42z = 0 + -1
42z = 0 + -1

Combine like terms: 0 + -1 = -1
42z = -1

Divide each side by '42'.
z = -0.02380952381

Simplifying
z = -0.02380952381
Solution
z = {0, -0.02380952381}