X^2-20X-189=0

Solution for X^2-20X-189=0 equation:

Simplifying
X2 + -20X + -189 = 0

Reorder the terms:
-189 + -20X + X2 = 0

Solving
-189 + -20X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-7 + -1X)(27 + -1X) = 0

Subproblem 1
Set the factor '(-7 + -1X)' equal to zero and attempt to solve:

Simplifying
-7 + -1X = 0

Solving
-7 + -1X = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1X = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1X = 0 + 7
-1X = 0 + 7

Combine like terms: 0 + 7 = 7
-1X = 7

Divide each side by '-1'.
X = -7

Simplifying
X = -7
Subproblem 2
Set the factor '(27 + -1X)' equal to zero and attempt to solve:

Simplifying
27 + -1X = 0

Solving
27 + -1X = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1X = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1X = 0 + -27
-1X = 0 + -27

Combine like terms: 0 + -27 = -27
-1X = -27

Divide each side by '-1'.
X = 27

Simplifying
X = 27
Solution
X = {-7, 27}