8a^2-16a=6a+12

Solution for 8a^2-16a=6a+12 equation:

Simplifying
8a2 + -16a = 6a + 12

Reorder the terms:
-16a + 8a2 = 6a + 12

Reorder the terms:
-16a + 8a2 = 12 + 6a

Solving
-16a + 8a2 = 12 + 6a

Solving for variable 'a'.

Reorder the terms:
-12 + -16a + -6a + 8a2 = 12 + 6a + -12 + -6a

Combine like terms: -16a + -6a = -22a
-12 + -22a + 8a2 = 12 + 6a + -12 + -6a

Reorder the terms:
-12 + -22a + 8a2 = 12 + -12 + 6a + -6a

Combine like terms: 12 + -12 = 0
-12 + -22a + 8a2 = 0 + 6a + -6a
-12 + -22a + 8a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-12 + -22a + 8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -11a + 4a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -11a + 4a2)' equal to zero and attempt to solve:

Simplifying
-6 + -11a + 4a2 = 0

Solving
-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}
Solution
a = {3.216364983, -0.466364983}