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

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

Simplifying
x3 + 2x2 + x = 4x

Reorder the terms:
x + 2x2 + x3 = 4x

Solving
x + 2x2 + x3 = 4x

Solving for variable 'x'.

Reorder the terms:
x + -4x + 2x2 + x3 = 4x + -4x

Combine like terms: x + -4x = -3x
-3x + 2x2 + x3 = 4x + -4x

Combine like terms: 4x + -4x = 0
-3x + 2x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 2x + x2) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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, -3, 1}