(2a^2-6a-3)=

Solution for (2a^2-6a-3)= equation:

Simplifying
(2a2 + -6a + -3) = 0

Reorder the terms:
(-3 + -6a + 2a2) = 0

Remove parenthesis around (-3 + -6a + 2a2)
-3 + -6a + 2a2 = 0

Solving
-3 + -6a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-1.5 + -3a + a2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -3a + 1.5 + a2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -3a + a2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3a + a2 = 0 + 1.5
-3a + a2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-3a + a2 = 1.5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 1.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 1.5 + 2.25

Combine like terms: 1.5 + 2.25 = 3.75
2.25 + -3a + a2 = 3.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
a + -1.5 = 1.936491673

Simplifying
a + -1.5 = 1.936491673

Reorder the terms:
-1.5 + a = 1.936491673

Solving
-1.5 + a = 1.936491673

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = 1.936491673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 1.936491673 + 1.5
a = 1.936491673 + 1.5

Combine like terms: 1.936491673 + 1.5 = 3.436491673
a = 3.436491673

Simplifying
a = 3.436491673

Subproblem 2
a + -1.5 = -1.936491673

Simplifying
a + -1.5 = -1.936491673

Reorder the terms:
-1.5 + a = -1.936491673

Solving
-1.5 + a = -1.936491673

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = -1.936491673 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -1.936491673 + 1.5
a = -1.936491673 + 1.5

Combine like terms: -1.936491673 + 1.5 = -0.436491673
a = -0.436491673

Simplifying
a = -0.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.436491673, -0.436491673}