6m^2-9m-3=0

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

Simplifying
6m2 + -9m + -3 = 0

Reorder the terms:
-3 + -9m + 6m2 = 0

Solving
-3 + -9m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -3m + 2m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -3m + 2m2)' equal to zero and attempt to solve:

Simplifying
-1 + -3m + 2m2 = 0

Solving
-1 + -3m + 2m2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + -1.5m + m2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.5m + 0.5 + m2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.5m + m2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.5m + m2 = 0 + 0.5
-1.5m + m2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.5m + m2 = 0.5

The m term is -1.5m.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5m + 0.5625 + m2 = 0.5 + 0.5625

Reorder the terms:
0.5625 + -1.5m + m2 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + -1.5m + m2 = 1.0625

Factor a perfect square on the left side:
(m + -0.75)(m + -0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(m + -0.75) equal to 1.030776406 and -1.030776406.

Subproblem 1
m + -0.75 = 1.030776406

Simplifying
m + -0.75 = 1.030776406

Reorder the terms:
-0.75 + m = 1.030776406

Solving
-0.75 + m = 1.030776406

Solving for variable 'm'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + m = 1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + m = 1.030776406 + 0.75
m = 1.030776406 + 0.75

Combine like terms: 1.030776406 + 0.75 = 1.780776406
m = 1.780776406

Simplifying
m = 1.780776406

Subproblem 2
m + -0.75 = -1.030776406

Simplifying
m + -0.75 = -1.030776406

Reorder the terms:
-0.75 + m = -1.030776406

Solving
-0.75 + m = -1.030776406

Solving for variable 'm'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + m = -1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + m = -1.030776406 + 0.75
m = -1.030776406 + 0.75

Combine like terms: -1.030776406 + 0.75 = -0.280776406
m = -0.280776406

Simplifying
m = -0.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.780776406, -0.280776406}
Solution
m = {1.780776406, -0.280776406}