2z=-7z^2

Solution for 2z=-7z^2 equation:

Simplifying
2z = -7z2

Solving
2z = -7z2

Solving for variable 'z'.

Combine like terms: -7z2 + 7z2 = 0
2z + 7z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(2 + 7z) = 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 '(2 + 7z)' equal to zero and attempt to solve:

Simplifying
2 + 7z = 0

Solving
2 + 7z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7z = 0 + -2
7z = 0 + -2

Combine like terms: 0 + -2 = -2
7z = -2

Divide each side by '7'.
z = -0.2857142857

Simplifying
z = -0.2857142857
Solution
z = {0, -0.2857142857}