25x^4+7x^3+6x^2=0

Solution for 25x^4+7x^3+6x^2=0 equation:

Simplifying
25x4 + 7x3 + 6x2 = 0

Reorder the terms:
6x2 + 7x3 + 25x4 = 0

Solving
6x2 + 7x3 + 25x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + 7x + 25x2) = 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 '(6 + 7x + 25x2)' equal to zero and attempt to solve:

Simplifying
6 + 7x + 25x2 = 0

Solving
6 + 7x + 25x2 = 0

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

Divide each side by '25'.
0.24 + 0.28x + x2 = 0

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + 0.28x + -0.24 + x2 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + 0.28x + x2 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + 0.28x + x2 = 0 + -0.24
0.28x + x2 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
0.28x + x2 = -0.24

The x term is 0.28x.  Take half its coefficient (0.14).
Square it (0.0196) and add it to both sides.

Add '0.0196' to each side of the equation.
0.28x + 0.0196 + x2 = -0.24 + 0.0196

Reorder the terms:
0.0196 + 0.28x + x2 = -0.24 + 0.0196

Combine like terms: -0.24 + 0.0196 = -0.2204
0.0196 + 0.28x + x2 = -0.2204

Factor a perfect square on the left side:
(x + 0.14)(x + 0.14) = -0.2204

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}