(x^3+4x^2+4x+3)=x+3

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

Simplifying
(x3 + 4x2 + 4x + 3) = x + 3

Reorder the terms:
(3 + 4x + 4x2 + x3) = x + 3

Remove parenthesis around (3 + 4x + 4x2 + x3)
3 + 4x + 4x2 + x3 = x + 3

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

Add '-3' to each side of the equation.
3 + 4x + 4x2 + -3 + x3 = 3 + -3 + x

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

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

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

Solving
4x + 4x2 + x3 = x

Solving for variable 'x'.

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

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

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

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

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

Simplifying
3 + x = 0

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

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

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, -3, -1}