x^4+10x^2=6x^3

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Solution for x^4+10x^2=6x^3 equation: 


Simplifying
x4 + 10x2 = 6x3

Reorder the terms:
10x2 + x4 = 6x3

Solving
10x2 + x4 = 6x3

Solving for variable 'x'.

Reorder the terms:
10x2 + -6x3 + x4 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
10x2 + -6x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(10 + -6x + x2) = 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 '(10 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -6x + x2 = 0

Solving
10 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -6x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -6x + x2 = 0 + -10
-6x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-6x + x2 = -10

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -10 + 9

Reorder the terms:
9 + -6x + x2 = -10 + 9

Combine like terms: -10 + 9 = -1
9 + -6x + x2 = -1

Factor a perfect square on the left side:
(x + -3)(x + -3) = -1

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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