[x+2][x+7]=36

Solution for [x+2][x+7]=36 equation:

Simplifying
[x + 2][x + 7] = 36

Reorder the terms:
[2 + x][x + 7] = 36

Reorder the terms:
[2 + x][7 + x] = 36

Multiply [2 + x] * [7 + x]
[2[7 + x] + x[7 + x]] = 36
[[7 * 2 + x * 2] + x[7 + x]] = 36
[[14 + 2x] + x[7 + x]] = 36
[14 + 2x + [7 * x + x * x]] = 36
[14 + 2x + [7x + x2]] = 36

Combine like terms: 2x + 7x = 9x
[14 + 9x + x2] = 36

Solving
14 + 9x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
14 + -36 + 9x + x2 = 36 + -36

Combine like terms: 14 + -36 = -22
-22 + 9x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-22 + 9x + x2 = 0

Factor a trinomial.
(-11 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-11, 2}