5a-6=4(a+1)12a+2

Solution for 5a-6=4(a+1)12a+2 equation:

Simplifying
5a + -6 = 4(a + 1) * 12a + 2

Reorder the terms:
-6 + 5a = 4(a + 1) * 12a + 2

Reorder the terms:
-6 + 5a = 4(1 + a) * 12a + 2

Reorder the terms for easier multiplication:
-6 + 5a = 4 * 12a(1 + a) + 2

Multiply 4 * 12
-6 + 5a = 48a(1 + a) + 2
-6 + 5a = (1 * 48a + a * 48a) + 2
-6 + 5a = (48a + 48a2) + 2

Reorder the terms:
-6 + 5a = 2 + 48a + 48a2

Solving
-6 + 5a = 2 + 48a + 48a2

Solving for variable 'a'.

Reorder the terms:
-6 + -2 + 5a + -48a + -48a2 = 2 + 48a + 48a2 + -2 + -48a + -48a2

Combine like terms: -6 + -2 = -8
-8 + 5a + -48a + -48a2 = 2 + 48a + 48a2 + -2 + -48a + -48a2

Combine like terms: 5a + -48a = -43a
-8 + -43a + -48a2 = 2 + 48a + 48a2 + -2 + -48a + -48a2

Reorder the terms:
-8 + -43a + -48a2 = 2 + -2 + 48a + -48a + 48a2 + -48a2

Combine like terms: 2 + -2 = 0
-8 + -43a + -48a2 = 0 + 48a + -48a + 48a2 + -48a2
-8 + -43a + -48a2 = 48a + -48a + 48a2 + -48a2

Combine like terms: 48a + -48a = 0
-8 + -43a + -48a2 = 0 + 48a2 + -48a2
-8 + -43a + -48a2 = 48a2 + -48a2

Combine like terms: 48a2 + -48a2 = 0
-8 + -43a + -48a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 43a + 48a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + 43a + 48a2)' equal to zero and attempt to solve:

Simplifying
8 + 43a + 48a2 = 0

Solving
8 + 43a + 48a2 = 0

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

Divide each side by '48'.
0.1666666667 + 0.8958333333a + a2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.8958333333a + -0.1666666667 + a2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.8958333333a + a2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.8958333333a + a2 = 0 + -0.1666666667
0.8958333333a + a2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.8958333333a + a2 = -0.1666666667

The a term is 0.8958333333a.  Take half its coefficient (0.4479166667).
Square it (0.2006293403) and add it to both sides.

Add '0.2006293403' to each side of the equation.
0.8958333333a + 0.2006293403 + a2 = -0.1666666667 + 0.2006293403

Reorder the terms:
0.2006293403 + 0.8958333333a + a2 = -0.1666666667 + 0.2006293403

Combine like terms: -0.1666666667 + 0.2006293403 = 0.0339626736
0.2006293403 + 0.8958333333a + a2 = 0.0339626736

Factor a perfect square on the left side:
(a + 0.4479166667)(a + 0.4479166667) = 0.0339626736

Calculate the square root of the right side: 0.184289646

Break this problem into two subproblems by setting 
(a + 0.4479166667) equal to 0.184289646 and -0.184289646.

Subproblem 1
a + 0.4479166667 = 0.184289646

Simplifying
a + 0.4479166667 = 0.184289646

Reorder the terms:
0.4479166667 + a = 0.184289646

Solving
0.4479166667 + a = 0.184289646

Solving for variable 'a'.

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

Add '-0.4479166667' to each side of the equation.
0.4479166667 + -0.4479166667 + a = 0.184289646 + -0.4479166667

Combine like terms: 0.4479166667 + -0.4479166667 = 0.0000000000
0.0000000000 + a = 0.184289646 + -0.4479166667
a = 0.184289646 + -0.4479166667

Combine like terms: 0.184289646 + -0.4479166667 = -0.2636270207
a = -0.2636270207

Simplifying
a = -0.2636270207

Subproblem 2
a + 0.4479166667 = -0.184289646

Simplifying
a + 0.4479166667 = -0.184289646

Reorder the terms:
0.4479166667 + a = -0.184289646

Solving
0.4479166667 + a = -0.184289646

Solving for variable 'a'.

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

Add '-0.4479166667' to each side of the equation.
0.4479166667 + -0.4479166667 + a = -0.184289646 + -0.4479166667

Combine like terms: 0.4479166667 + -0.4479166667 = 0.0000000000
0.0000000000 + a = -0.184289646 + -0.4479166667
a = -0.184289646 + -0.4479166667

Combine like terms: -0.184289646 + -0.4479166667 = -0.6322063127
a = -0.6322063127

Simplifying
a = -0.6322063127

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.2636270207, -0.6322063127}
Solution
a = {-0.2636270207, -0.6322063127}