10x^4+20x^3+15x^2=0

Solution for 10x^4+20x^3+15x^2=0 equation:

Simplifying
10x4 + 20x3 + 15x2 = 0

Reorder the terms:
15x2 + 20x3 + 10x4 = 0

Solving
15x2 + 20x3 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(3 + 4x + 2x2) = 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 '(3 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x + 2x2 = 0

Solving
3 + 4x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 2x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 2x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2x + x2 = 0 + -1.5
2x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2x + x2 = -1.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -1.5 + 1

Reorder the terms:
1 + 2x + x2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + 2x + x2 = -0.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -0.5

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}