x^4+x^2=2x^3

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

Simplifying
x4 + x2 = 2x3

Reorder the terms:
x2 + x4 = 2x3

Solving
x2 + x4 = 2x3

Solving for variable 'x'.

Reorder the terms:
x2 + -2x3 + x4 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
x2 + -2x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + -2x + x2) = 0

Factor a trinomial.
x2((1 + -1x)(1 + -1x)) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1, 1}