(x-20)(x+9)=0

Solution for (x-20)(x+9)=0 equation:

Simplifying
(x + -20)(x + 9) = 0

Reorder the terms:
(-20 + x)(x + 9) = 0

Reorder the terms:
(-20 + x)(9 + x) = 0

Multiply (-20 + x) * (9 + x)
(-20(9 + x) + x(9 + x)) = 0
((9 * -20 + x * -20) + x(9 + x)) = 0
((-180 + -20x) + x(9 + x)) = 0
(-180 + -20x + (9 * x + x * x)) = 0
(-180 + -20x + (9x + x2)) = 0

Combine like terms: -20x + 9x = -11x
(-180 + -11x + x2) = 0

Solving
-180 + -11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 20}