6X-X^2-9=0

Solution for 6X-X^2-9=0 equation:

Simplifying
6X + -1X2 + -9 = 0

Reorder the terms:
-9 + 6X + -1X2 = 0

Solving
-9 + 6X + -1X2 = 0

Solving for variable 'X'.

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

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

Simplifying
-3 + X = 0

Solving
-3 + X = 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 + X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + X = 0 + 3
X = 0 + 3

Combine like terms: 0 + 3 = 3
X = 3

Simplifying
X = 3
Subproblem 2
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
Solution
X = {3, 3}