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

Solution for 2(a-3)(2a+1)=a equation:

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

Reorder the terms:
2(-3 + a)(2a + 1) = a

Reorder the terms:
2(-3 + a)(1 + 2a) = a

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

Combine like terms: -6a + 1a = -5a
2(-3 + -5a + 2a2) = a
(-3 * 2 + -5a * 2 + 2a2 * 2) = a
(-6 + -10a + 4a2) = a

Solving
-6 + -10a + 4a2 = a

Solving for variable 'a'.

Reorder the terms:
-6 + -10a + -1a + 4a2 = a + -1a

Combine like terms: -10a + -1a = -11a
-6 + -11a + 4a2 = a + -1a

Combine like terms: a + -1a = 0
-6 + -11a + 4a2 = 0

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

Divide each side by '4'.
-1.5 + -2.75a + a2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.75a + 1.5 + a2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.75a + a2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.75a + a2 = 0 + 1.5
-2.75a + a2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2.75a + a2 = 1.5

The a term is -2.75a.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75a + 1.890625 + a2 = 1.5 + 1.890625

Reorder the terms:
1.890625 + -2.75a + a2 = 1.5 + 1.890625

Combine like terms: 1.5 + 1.890625 = 3.390625
1.890625 + -2.75a + a2 = 3.390625

Factor a perfect square on the left side:
(a + -1.375)(a + -1.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(a + -1.375) equal to 1.841364983 and -1.841364983.

Subproblem 1
a + -1.375 = 1.841364983

Simplifying
a + -1.375 = 1.841364983

Reorder the terms:
-1.375 + a = 1.841364983

Solving
-1.375 + a = 1.841364983

Solving for variable 'a'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + a = 1.841364983 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + a = 1.841364983 + 1.375
a = 1.841364983 + 1.375

Combine like terms: 1.841364983 + 1.375 = 3.216364983
a = 3.216364983

Simplifying
a = 3.216364983

Subproblem 2
a + -1.375 = -1.841364983

Simplifying
a + -1.375 = -1.841364983

Reorder the terms:
-1.375 + a = -1.841364983

Solving
-1.375 + a = -1.841364983

Solving for variable 'a'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + a = -1.841364983 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + a = -1.841364983 + 1.375
a = -1.841364983 + 1.375

Combine like terms: -1.841364983 + 1.375 = -0.466364983
a = -0.466364983

Simplifying
a = -0.466364983

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.216364983, -0.466364983}