(x^3+x^2+x+1)(19x-19)=0

Solution for (x^3+x^2+x+1)(19x-19)=0 equation:

Simplifying
(x3 + x2 + x + 1)(19x + -19) = 0

Reorder the terms:
(1 + x + x2 + x3)(19x + -19) = 0

Reorder the terms:
(1 + x + x2 + x3)(-19 + 19x) = 0

Multiply (1 + x + x2 + x3) * (-19 + 19x)
(1(-19 + 19x) + x(-19 + 19x) + x2(-19 + 19x) + x3(-19 + 19x)) = 0
((-19 * 1 + 19x * 1) + x(-19 + 19x) + x2(-19 + 19x) + x3(-19 + 19x)) = 0
((-19 + 19x) + x(-19 + 19x) + x2(-19 + 19x) + x3(-19 + 19x)) = 0
(-19 + 19x + (-19 * x + 19x * x) + x2(-19 + 19x) + x3(-19 + 19x)) = 0
(-19 + 19x + (-19x + 19x2) + x2(-19 + 19x) + x3(-19 + 19x)) = 0
(-19 + 19x + -19x + 19x2 + (-19 * x2 + 19x * x2) + x3(-19 + 19x)) = 0
(-19 + 19x + -19x + 19x2 + (-19x2 + 19x3) + x3(-19 + 19x)) = 0
(-19 + 19x + -19x + 19x2 + -19x2 + 19x3 + (-19 * x3 + 19x * x3)) = 0
(-19 + 19x + -19x + 19x2 + -19x2 + 19x3 + (-19x3 + 19x4)) = 0

Combine like terms: 19x + -19x = 0
(-19 + 0 + 19x2 + -19x2 + 19x3 + -19x3 + 19x4) = 0
(-19 + 19x2 + -19x2 + 19x3 + -19x3 + 19x4) = 0

Combine like terms: 19x2 + -19x2 = 0
(-19 + 0 + 19x3 + -19x3 + 19x4) = 0
(-19 + 19x3 + -19x3 + 19x4) = 0

Combine like terms: 19x3 + -19x3 = 0
(-19 + 0 + 19x4) = 0
(-19 + 19x4) = 0

Solving
-19 + 19x4 = 0

Solving for variable 'x'.

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

Add '19' to each side of the equation.
-19 + 19 + 19x4 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 19x4 = 0 + 19
19x4 = 0 + 19

Combine like terms: 0 + 19 = 19
19x4 = 19

Divide each side by '19'.
x4 = 1

Simplifying
x4 = 1

Reorder the terms:
-1 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x4 = 0

Factor a difference between two squares.
(1 + x2)(-1 + x2) = 0

Factor a difference between two squares.
(1 + x2)((1 + x)(-1 + x)) = 0

Subproblem 1
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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
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 = {-1, 1}