(x^2+x+1)3+x^2+4x=

Solution for (x^2+x+1)3+x^2+4x= equation:

Simplifying
(x2 + x + 1) * 3 + x2 + 4x = 0

Reorder the terms:
(1 + x + x2) * 3 + x2 + 4x = 0

Reorder the terms for easier multiplication:
3(1 + x + x2) + x2 + 4x = 0
(1 * 3 + x * 3 + x2 * 3) + x2 + 4x = 0
(3 + 3x + 3x2) + x2 + 4x = 0

Reorder the terms:
3 + 3x + 4x + 3x2 + x2 = 0

Combine like terms: 3x + 4x = 7x
3 + 7x + 3x2 + x2 = 0

Combine like terms: 3x2 + x2 = 4x2
3 + 7x + 4x2 = 0

Solving
3 + 7x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + x)(3 + 4x) = 0

Subproblem 1
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 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-1, -0.75}