4x^3+3x^2=x

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

Simplifying
4x3 + 3x2 = x

Reorder the terms:
3x2 + 4x3 = x

Solving
3x2 + 4x3 = x

Solving for variable 'x'.

Reorder the terms:
-1x + 3x2 + 4x3 = x + -1x

Combine like terms: x + -1x = 0
-1x + 3x2 + 4x3 = 0

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

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, -1, 0.25}