(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}