(x-20)(x+3)=0

Solution for (x-20)(x+3)=0 equation:

Simplifying
(x + -20)(x + 3) = 0

Reorder the terms:
(-20 + x)(x + 3) = 0

Reorder the terms:
(-20 + x)(3 + x) = 0

Multiply (-20 + x) * (3 + x)
(-20(3 + x) + x(3 + x)) = 0
((3 * -20 + x * -20) + x(3 + x)) = 0
((-60 + -20x) + x(3 + x)) = 0
(-60 + -20x + (3 * x + x * x)) = 0
(-60 + -20x + (3x + x2)) = 0

Combine like terms: -20x + 3x = -17x
(-60 + -17x + x2) = 0

Solving
-60 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 20}