10x^3+15x^4+(3x^2)=0

Solution for 10x^3+15x^4+(3x^2)=0 equation:

Simplifying
10x3 + 15x4 + (3x2) = 0

Reorder the terms:
(3x2) + 10x3 + 15x4 = 0

Solving
(3x2) + 10x3 + 15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3 + 10x + 15x2) = 0

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 '(3 + 10x + 15x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + 15x2 = 0

Solving
3 + 10x + 15x2 = 0

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

Divide each side by '15'.
0.2 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.6666666667x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.6666666667x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.6666666667x + x2 = 0 + -0.2
0.6666666667x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
0.6666666667x + x2 = -0.2

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -0.2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -0.2 + 0.1111111112

Combine like terms: -0.2 + 0.1111111112 = -0.0888888888
0.1111111112 + 0.6666666667x + x2 = -0.0888888888

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = -0.0888888888

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}