12X-X^2-20=0

Solution for 12X-X^2-20=0 equation:

Simplifying
12X + -1X2 + -20 = 0

Reorder the terms:
-20 + 12X + -1X2 = 0

Solving
-20 + 12X + -1X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-10 + X)(2 + -1X) = 0

Subproblem 1
Set the factor '(-10 + X)' equal to zero and attempt to solve:

Simplifying
-10 + X = 0

Solving
-10 + X = 0

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

Add '10' to each side of the equation.
-10 + 10 + X = 0 + 10

Combine like terms: -10 + 10 = 0
0 + X = 0 + 10
X = 0 + 10

Combine like terms: 0 + 10 = 10
X = 10

Simplifying
X = 10
Subproblem 2
Set the factor '(2 + -1X)' equal to zero and attempt to solve:

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {10, 2}