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

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

Simplifying
(2 + -1a)(3 + 2a) = 2a + -6

Multiply (2 + -1a) * (3 + 2a)
(2(3 + 2a) + -1a * (3 + 2a)) = 2a + -6
((3 * 2 + 2a * 2) + -1a * (3 + 2a)) = 2a + -6
((6 + 4a) + -1a * (3 + 2a)) = 2a + -6
(6 + 4a + (3 * -1a + 2a * -1a)) = 2a + -6
(6 + 4a + (-3a + -2a2)) = 2a + -6

Combine like terms: 4a + -3a = 1a
(6 + 1a + -2a2) = 2a + -6

Reorder the terms:
6 + 1a + -2a2 = -6 + 2a

Solving
6 + 1a + -2a2 = -6 + 2a

Solving for variable 'a'.

Reorder the terms:
6 + 6 + 1a + -2a + -2a2 = -6 + 2a + 6 + -2a

Combine like terms: 6 + 6 = 12
12 + 1a + -2a + -2a2 = -6 + 2a + 6 + -2a

Combine like terms: 1a + -2a = -1a
12 + -1a + -2a2 = -6 + 2a + 6 + -2a

Reorder the terms:
12 + -1a + -2a2 = -6 + 6 + 2a + -2a

Combine like terms: -6 + 6 = 0
12 + -1a + -2a2 = 0 + 2a + -2a
12 + -1a + -2a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
12 + -1a + -2a2 = 0

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

Divide each side by '-2'.
-6 + 0.5a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.5a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.5a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.5a + a2 = 0 + 6
0.5a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.5a + a2 = 6

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = 6 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + 0.5a + a2 = 6.0625

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(a + 0.25) equal to 2.46221445 and -2.46221445.

Subproblem 1
a + 0.25 = 2.46221445

Simplifying
a + 0.25 = 2.46221445

Reorder the terms:
0.25 + a = 2.46221445

Solving
0.25 + a = 2.46221445

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = 2.46221445 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = 2.46221445 + -0.25
a = 2.46221445 + -0.25

Combine like terms: 2.46221445 + -0.25 = 2.21221445
a = 2.21221445

Simplifying
a = 2.21221445

Subproblem 2
a + 0.25 = -2.46221445

Simplifying
a + 0.25 = -2.46221445

Reorder the terms:
0.25 + a = -2.46221445

Solving
0.25 + a = -2.46221445

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = -2.46221445 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = -2.46221445 + -0.25
a = -2.46221445 + -0.25

Combine like terms: -2.46221445 + -0.25 = -2.71221445
a = -2.71221445

Simplifying
a = -2.71221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.21221445, -2.71221445}