(x+2)(5-x)=0

Solution for (x+2)(5-x)=0 equation:

Simplifying
(x + 2)(5 + -1x) = 0

Reorder the terms:
(2 + x)(5 + -1x) = 0

Multiply (2 + x) * (5 + -1x)
(2(5 + -1x) + x(5 + -1x)) = 0
((5 * 2 + -1x * 2) + x(5 + -1x)) = 0
((10 + -2x) + x(5 + -1x)) = 0
(10 + -2x + (5 * x + -1x * x)) = 0
(10 + -2x + (5x + -1x2)) = 0

Combine like terms: -2x + 5x = 3x
(10 + 3x + -1x2) = 0

Solving
10 + 3x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {5, -2}