(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.
(-6 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 5}