4(x+1)+x(x+1)=

Solution for 4(x+1)+x(x+1)= equation:

Simplifying
4(x + 1) + x(x + 1) = 0

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

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

Combine like terms: 4x + 1x = 5x
4 + 5x + x2 = 0

Solving
4 + 5x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
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
Solution
x = {-4, -1}