(x-13)(x+20)=0

Solution for (x-13)(x+20)=0 equation:

Simplifying
(x + -13)(x + 20) = 0

Reorder the terms:
(-13 + x)(x + 20) = 0

Reorder the terms:
(-13 + x)(20 + x) = 0

Multiply (-13 + x) * (20 + x)
(-13(20 + x) + x(20 + x)) = 0
((20 * -13 + x * -13) + x(20 + x)) = 0
((-260 + -13x) + x(20 + x)) = 0
(-260 + -13x + (20 * x + x * x)) = 0
(-260 + -13x + (20x + x2)) = 0

Combine like terms: -13x + 20x = 7x
(-260 + 7x + x2) = 0

Solving
-260 + 7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-20 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
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
Solution
x = {-20, 13}