4x^4+20x^3+60x^2=

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Solution for 4x^4+20x^3+60x^2= equation: 


Simplifying
4x4 + 20x3 + 60x2 = 0

Reorder the terms:
60x2 + 20x3 + 4x4 = 0

Solving
60x2 + 20x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(15 + 5x + x2) = 0

Ignore the factor 4.

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 '(15 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 5x + x2 = 0

Solving
15 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 5x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 5x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 5x + x2 = 0 + -15
5x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
5x + x2 = -15

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -15 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -15 + 6.25

Combine like terms: -15 + 6.25 = -8.75
6.25 + 5x + x2 = -8.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -8.75

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}

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