(x+4)(13-x)=0

Solution for (x+4)(13-x)=0 equation:

Simplifying
(x + 4)(13 + -1x) = 0

Reorder the terms:
(4 + x)(13 + -1x) = 0

Multiply (4 + x) * (13 + -1x)
(4(13 + -1x) + x(13 + -1x)) = 0
((13 * 4 + -1x * 4) + x(13 + -1x)) = 0
((52 + -4x) + x(13 + -1x)) = 0
(52 + -4x + (13 * x + -1x * x)) = 0
(52 + -4x + (13x + -1x2)) = 0

Combine like terms: -4x + 13x = 9x
(52 + 9x + -1x2) = 0

Solving
52 + 9x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {13, -4}