(13x+x^2)-(x+13)=0

Solution for (13x+x^2)-(x+13)=0 equation:

Simplifying
(13x + x2) + -1(x + 13) = 0

Remove parenthesis around (13x + x2)
13x + x2 + -1(x + 13) = 0

Reorder the terms:
13x + x2 + -1(13 + x) = 0
13x + x2 + (13 * -1 + x * -1) = 0
13x + x2 + (-13 + -1x) = 0

Reorder the terms:
-13 + 13x + -1x + x2 = 0

Combine like terms: 13x + -1x = 12x
-13 + 12x + x2 = 0

Solving
-13 + 12x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -1x)(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-13, 1}