3x^4+4x^2=13x^3

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Solution for 3x^4+4x^2=13x^3 equation: 


Simplifying
3x4 + 4x2 = 13x3

Reorder the terms:
4x2 + 3x4 = 13x3

Solving
4x2 + 3x4 = 13x3

Solving for variable 'x'.

Reorder the terms:
4x2 + -13x3 + 3x4 = 13x3 + -13x3

Combine like terms: 13x3 + -13x3 = 0
4x2 + -13x3 + 3x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -13x + 3x2) = 0

Factor a trinomial.
x2((1 + -3x)(4 + -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 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 0.3333333333, 4}

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