3X^2-9X-54=

Solution for 3X^2-9X-54= equation:

Simplifying
3X2 + -9X + -54 = 0

Reorder the terms:
-54 + -9X + 3X2 = 0

Solving
-54 + -9X + 3X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -3X + X2) = 0

Factor a trinomial.
3((-3 + -1X)(6 + -1X)) = 0

Ignore the factor 3.
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 '(6 + -1X)' equal to zero and attempt to solve:

Simplifying
6 + -1X = 0

Solving
6 + -1X = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X = 0 + -6
-1X = 0 + -6

Combine like terms: 0 + -6 = -6
-1X = -6

Divide each side by '-1'.
X = 6

Simplifying
X = 6
Solution
X = {-3, 6}