-4a^2-4a+6=9

Solution for -4a^2-4a+6=9 equation:

Simplifying
-4a2 + -4a + 6 = 9

Reorder the terms:
6 + -4a + -4a2 = 9

Solving
6 + -4a + -4a2 = 9

Solving for variable 'a'.

Reorder the terms:
6 + -9 + -4a + -4a2 = 9 + -9

Combine like terms: 6 + -9 = -3
-3 + -4a + -4a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-3 + -4a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4a + 4a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 4a + 4a2)' equal to zero and attempt to solve:

Simplifying
3 + 4a + 4a2 = 0

Solving
3 + 4a + 4a2 = 0

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

Divide each side by '4'.
0.75 + a + a2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + a + -0.75 + a2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + a + a2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + a + a2 = 0 + -0.75
a + a2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
a + a2 = -0.75

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = -0.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = -0.75 + 0.25

Combine like terms: -0.75 + 0.25 = -0.5
1.25 + a2 = -0.5

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -0.5

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.