3x^3+x=4x^2

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

Simplifying
3x3 + x = 4x2

Reorder the terms:
x + 3x3 = 4x2

Solving
x + 3x3 = 4x2

Solving for variable 'x'.

Reorder the terms:
x + -4x2 + 3x3 = 4x2 + -4x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -4x + 3x2) = 0

Factor a trinomial.
x((1 + -3x)(1 + -1x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
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 '(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, 0.3333333333, 1}