(x-6)(x+20)=0

Solution for (x-6)(x+20)=0 equation:

Simplifying
(x + -6)(x + 20) = 0

Reorder the terms:
(-6 + x)(x + 20) = 0

Reorder the terms:
(-6 + x)(20 + x) = 0

Multiply (-6 + x) * (20 + x)
(-6(20 + x) + x(20 + x)) = 0
((20 * -6 + x * -6) + x(20 + x)) = 0
((-120 + -6x) + x(20 + x)) = 0
(-120 + -6x + (20 * x + x * x)) = 0
(-120 + -6x + (20x + x2)) = 0

Combine like terms: -6x + 20x = 14x
(-120 + 14x + x2) = 0

Solving
-120 + 14x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-20 + -1x)(6 + -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 '(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
Solution
x = {-20, 6}