2(4a-12)3a=6a+1

Solution for 2(4a-12)3a=6a+1 equation:

Simplifying
2(4a + -12) * 3a = 6a + 1

Reorder the terms:
2(-12 + 4a) * 3a = 6a + 1

Reorder the terms for easier multiplication:
2 * 3a(-12 + 4a) = 6a + 1

Multiply 2 * 3
6a(-12 + 4a) = 6a + 1
(-12 * 6a + 4a * 6a) = 6a + 1
(-72a + 24a2) = 6a + 1

Reorder the terms:
-72a + 24a2 = 1 + 6a

Solving
-72a + 24a2 = 1 + 6a

Solving for variable 'a'.

Reorder the terms:
-1 + -72a + -6a + 24a2 = 1 + 6a + -1 + -6a

Combine like terms: -72a + -6a = -78a
-1 + -78a + 24a2 = 1 + 6a + -1 + -6a

Reorder the terms:
-1 + -78a + 24a2 = 1 + -1 + 6a + -6a

Combine like terms: 1 + -1 = 0
-1 + -78a + 24a2 = 0 + 6a + -6a
-1 + -78a + 24a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-1 + -78a + 24a2 = 0

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

Divide each side by '24'.
-0.04166666667 + -3.25a + a2 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + -3.25a + 0.04166666667 + a2 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + -3.25a + a2 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + -3.25a + a2 = 0 + 0.04166666667
-3.25a + a2 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
-3.25a + a2 = 0.04166666667

The a term is -3.25a.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25a + 2.640625 + a2 = 0.04166666667 + 2.640625

Reorder the terms:
2.640625 + -3.25a + a2 = 0.04166666667 + 2.640625

Combine like terms: 0.04166666667 + 2.640625 = 2.68229166667
2.640625 + -3.25a + a2 = 2.68229166667

Factor a perfect square on the left side:
(a + -1.625)(a + -1.625) = 2.68229166667

Calculate the square root of the right side: 1.637770334

Break this problem into two subproblems by setting 
(a + -1.625) equal to 1.637770334 and -1.637770334.

Subproblem 1
a + -1.625 = 1.637770334

Simplifying
a + -1.625 = 1.637770334

Reorder the terms:
-1.625 + a = 1.637770334

Solving
-1.625 + a = 1.637770334

Solving for variable 'a'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + a = 1.637770334 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + a = 1.637770334 + 1.625
a = 1.637770334 + 1.625

Combine like terms: 1.637770334 + 1.625 = 3.262770334
a = 3.262770334

Simplifying
a = 3.262770334

Subproblem 2
a + -1.625 = -1.637770334

Simplifying
a + -1.625 = -1.637770334

Reorder the terms:
-1.625 + a = -1.637770334

Solving
-1.625 + a = -1.637770334

Solving for variable 'a'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + a = -1.637770334 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + a = -1.637770334 + 1.625
a = -1.637770334 + 1.625

Combine like terms: -1.637770334 + 1.625 = -0.012770334
a = -0.012770334

Simplifying
a = -0.012770334

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.262770334, -0.012770334}