x^2+18x^2+6x=0

Solution for x^2+18x^2+6x=0 equation:

Simplifying
x2 + 18x2 + 6x = 0

Reorder the terms:
6x + x2 + 18x2 = 0

Combine like terms: x2 + 18x2 = 19x2
6x + 19x2 = 0

Solving
6x + 19x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + 19x) = 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 '(6 + 19x)' equal to zero and attempt to solve:

Simplifying
6 + 19x = 0

Solving
6 + 19x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 19x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 19x = 0 + -6
19x = 0 + -6

Combine like terms: 0 + -6 = -6
19x = -6

Divide each side by '19'.
x = -0.3157894737

Simplifying
x = -0.3157894737
Solution
x = {0, -0.3157894737}