[x+4][x-5]=10

Solution for [x+4][x-5]=10 equation:

Simplifying
[x + 4][x + -5] = 10

Reorder the terms:
[4 + x][x + -5] = 10

Reorder the terms:
[4 + x][-5 + x] = 10

Multiply [4 + x] * [-5 + x]
[4[-5 + x] + x[-5 + x]] = 10
[[-5 * 4 + x * 4] + x[-5 + x]] = 10
[[-20 + 4x] + x[-5 + x]] = 10
[-20 + 4x + [-5 * x + x * x]] = 10
[-20 + 4x + [-5x + x2]] = 10

Combine like terms: 4x + -5x = -1x
[-20 + -1x + x2] = 10

Solving
-20 + -1x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-20 + -10 + -1x + x2 = 10 + -10

Combine like terms: -20 + -10 = -30
-30 + -1x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-30 + -1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -1x) = 0

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-5, 6}