-6x^2-10x-6=0

Solution for -6x^2-10x-6=0 equation:

Simplifying
-6x2 + -10x + -6 = 0

Reorder the terms:
-6 + -10x + -6x2 = 0

Solving
-6 + -10x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 5x + 3x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + 5x + 3x2 = 0

Solving
3 + 5x + 3x2 = 0

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

Divide each side by '3'.
1 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 1.666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.666666667x + x2 = 0 + -1
1.666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.666666667x + x2 = -1

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -1 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -1 + 0.6944444447

Combine like terms: -1 + 0.6944444447 = -0.3055555553
0.6944444447 + 1.666666667x + x2 = -0.3055555553

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -0.3055555553

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.