x(x+4)+2(x+5)=5

Solution for x(x+4)+2(x+5)=5 equation:

Simplifying
x(x + 4) + 2(x + 5) = 5

Reorder the terms:
x(4 + x) + 2(x + 5) = 5
(4 * x + x * x) + 2(x + 5) = 5
(4x + x2) + 2(x + 5) = 5

Reorder the terms:
4x + x2 + 2(5 + x) = 5
4x + x2 + (5 * 2 + x * 2) = 5
4x + x2 + (10 + 2x) = 5

Reorder the terms:
10 + 4x + 2x + x2 = 5

Combine like terms: 4x + 2x = 6x
10 + 6x + x2 = 5

Solving
10 + 6x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
10 + -5 + 6x + x2 = 5 + -5

Combine like terms: 10 + -5 = 5
5 + 6x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
5 + 6x + x2 = 0

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

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
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 = {-5, -1}