9x^2=-x

Solution for 9x^2=-x equation:

Simplifying
9x2 = -1x

Solving
9x2 = -1x

Solving for variable 'x'.

Reorder the terms:
x + 9x2 = -1x + x

Combine like terms: -1x + x = 0
x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 9x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {0, -0.1111111111}