9X^2-6X-3=0

Solution for 9X^2-6X-3=0 equation:

Simplifying
9X2 + -6X + -3 = 0

Reorder the terms:
-3 + -6X + 9X2 = 0

Solving
-3 + -6X + 9X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2X + 3X2) = 0

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

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

Simplifying
-1 + -3X = 0

Solving
-1 + -3X = 0

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

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

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

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

Divide each side by '-3'.
X = -0.3333333333

Simplifying
X = -0.3333333333
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
Solution
X = {-0.3333333333, 1}