50x^2+x=0

Solution for 50x^2+x=0 equation:

Simplifying
50x2 + x = 0

Reorder the terms:
x + 50x2 = 0

Solving
x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 50x) = 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 + 50x)' equal to zero and attempt to solve:

Simplifying
1 + 50x = 0

Solving
1 + 50x = 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 + 50x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 50x = 0 + -1
50x = 0 + -1

Combine like terms: 0 + -1 = -1
50x = -1

Divide each side by '50'.
x = -0.02

Simplifying
x = -0.02
Solution
x = {0, -0.02}