(x^4+9x^3+20x^2+13x+6)=(x+6)

Solution for (x^4+9x^3+20x^2+13x+6)=(x+6) equation:

Simplifying
(x4 + 9x3 + 20x2 + 13x + 6) = (x + 6)

Reorder the terms:
(6 + 13x + 20x2 + 9x3 + x4) = (x + 6)

Remove parenthesis around (6 + 13x + 20x2 + 9x3 + x4)
6 + 13x + 20x2 + 9x3 + x4 = (x + 6)

Reorder the terms:
6 + 13x + 20x2 + 9x3 + x4 = (6 + x)

Remove parenthesis around (6 + x)
6 + 13x + 20x2 + 9x3 + x4 = 6 + x

Add '-6' to each side of the equation.
6 + 13x + 20x2 + 9x3 + -6 + x4 = 6 + -6 + x

Reorder the terms:
6 + -6 + 13x + 20x2 + 9x3 + x4 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
0 + 13x + 20x2 + 9x3 + x4 = 6 + -6 + x
13x + 20x2 + 9x3 + x4 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
13x + 20x2 + 9x3 + x4 = 0 + x
13x + 20x2 + 9x3 + x4 = x

Solving
13x + 20x2 + 9x3 + x4 = x

Solving for variable 'x'.

Reorder the terms:
13x + -1x + 20x2 + 9x3 + x4 = x + -1x

Combine like terms: 13x + -1x = 12x
12x + 20x2 + 9x3 + x4 = x + -1x

Combine like terms: x + -1x = 0
12x + 20x2 + 9x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + 20x + 9x2 + x3) = 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 '(12 + 20x + 9x2 + x3)' equal to zero and attempt to solve:

Simplifying
12 + 20x + 9x2 + x3 = 0

Solving
12 + 20x + 9x2 + x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}