-4x^2-9x-6=0

Solution for -4x^2-9x-6=0 equation:

Simplifying
-4x2 + -9x + -6 = 0

Reorder the terms:
-6 + -9x + -4x2 = 0

Solving
-6 + -9x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 9x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 9x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + 9x + 4x2 = 0

Solving
6 + 9x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 2.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 2.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2.25x + x2 = 0 + -1.5
2.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2.25x + x2 = -1.5

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = -1.5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = -1.5 + 1.265625

Combine like terms: -1.5 + 1.265625 = -0.234375
1.265625 + 2.25x + x2 = -0.234375

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.