(x-5)(x+4)=22

Solution for (x-5)(x+4)=22 equation:

Simplifying
(x + -5)(x + 4) = 22

Reorder the terms:
(-5 + x)(x + 4) = 22

Reorder the terms:
(-5 + x)(4 + x) = 22

Multiply (-5 + x) * (4 + x)
(-5(4 + x) + x(4 + x)) = 22
((4 * -5 + x * -5) + x(4 + x)) = 22
((-20 + -5x) + x(4 + x)) = 22
(-20 + -5x + (4 * x + x * x)) = 22
(-20 + -5x + (4x + x2)) = 22

Combine like terms: -5x + 4x = -1x
(-20 + -1x + x2) = 22

Solving
-20 + -1x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-20 + -22 + -1x + x2 = 22 + -22

Combine like terms: -20 + -22 = -42
-42 + -1x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-42 + -1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6, 7}