45x^4+5x^3+30x^2=0

Solution for 45x^4+5x^3+30x^2=0 equation:

Simplifying
45x4 + 5x3 + 30x2 = 0

Reorder the terms:
30x2 + 5x3 + 45x4 = 0

Solving
30x2 + 5x3 + 45x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(6 + x + 9x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6 + x + 9x2)' equal to zero and attempt to solve:

Simplifying
6 + x + 9x2 = 0

Solving
6 + x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
0.6666666667 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.1111111111x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.1111111111x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.1111111111x + x2 = 0 + -0.6666666667
0.1111111111x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.1111111111x + x2 = -0.6666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1111111111x + 0.25 + x2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.1111111111x + x2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + 0.1111111111x + x2 = -0.4166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.4166666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}