[x+2][x+5]=

Solution for [x+2][x+5]= equation:

Simplifying
[x + 2][x + 5] = 0

Reorder the terms:
[2 + x][x + 5] = 0

Reorder the terms:
[2 + x][5 + x] = 0

Multiply [2 + x] * [5 + x]
[2[5 + x] + x[5 + x]] = 0
[[5 * 2 + x * 2] + x[5 + x]] = 0
[[10 + 2x] + x[5 + x]] = 0
[10 + 2x + [5 * x + x * x]] = 0
[10 + 2x + [5x + x2]] = 0

Combine like terms: 2x + 5x = 7x
[10 + 7x + x2] = 0

Solving
10 + 7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-5, -2}