4x^4+11x^3+8x^2=0

Solution for 4x^4+11x^3+8x^2=0 equation:

Simplifying
4x4 + 11x3 + 8x2 = 0

Reorder the terms:
8x2 + 11x3 + 4x4 = 0

Solving
8x2 + 11x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(8 + 11x + 4x2) = 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 '(8 + 11x + 4x2)' equal to zero and attempt to solve:

Simplifying
8 + 11x + 4x2 = 0

Solving
8 + 11x + 4x2 = 0

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

Divide each side by '4'.
2 + 2.75x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.75x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 2.75x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.75x + x2 = 0 + -2
2.75x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.75x + x2 = -2

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = -2 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = -2 + 1.890625

Combine like terms: -2 + 1.890625 = -0.109375
1.890625 + 2.75x + x2 = -0.109375

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = -0.109375

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}