8a(1a-2)=5(a+6)

Solution for 8a(1a-2)=5(a+6) equation:

Simplifying
8a(1a + -2) = 5(a + 6)

Reorder the terms:
8a(-2 + 1a) = 5(a + 6)
(-2 * 8a + 1a * 8a) = 5(a + 6)
(-16a + 8a2) = 5(a + 6)

Reorder the terms:
-16a + 8a2 = 5(6 + a)
-16a + 8a2 = (6 * 5 + a * 5)
-16a + 8a2 = (30 + 5a)

Solving
-16a + 8a2 = 30 + 5a

Solving for variable 'a'.

Reorder the terms:
-30 + -16a + -5a + 8a2 = 30 + 5a + -30 + -5a

Combine like terms: -16a + -5a = -21a
-30 + -21a + 8a2 = 30 + 5a + -30 + -5a

Reorder the terms:
-30 + -21a + 8a2 = 30 + -30 + 5a + -5a

Combine like terms: 30 + -30 = 0
-30 + -21a + 8a2 = 0 + 5a + -5a
-30 + -21a + 8a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-30 + -21a + 8a2 = 0

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

Divide each side by '8'.
-3.75 + -2.625a + a2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -2.625a + 3.75 + a2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -2.625a + a2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -2.625a + a2 = 0 + 3.75
-2.625a + a2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-2.625a + a2 = 3.75

The a term is -2.625a.  Take half its coefficient (-1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
-2.625a + 1.72265625 + a2 = 3.75 + 1.72265625

Reorder the terms:
1.72265625 + -2.625a + a2 = 3.75 + 1.72265625

Combine like terms: 3.75 + 1.72265625 = 5.47265625
1.72265625 + -2.625a + a2 = 5.47265625

Factor a perfect square on the left side:
(a + -1.3125)(a + -1.3125) = 5.47265625

Calculate the square root of the right side: 2.339370909

Break this problem into two subproblems by setting 
(a + -1.3125) equal to 2.339370909 and -2.339370909.

Subproblem 1
a + -1.3125 = 2.339370909

Simplifying
a + -1.3125 = 2.339370909

Reorder the terms:
-1.3125 + a = 2.339370909

Solving
-1.3125 + a = 2.339370909

Solving for variable 'a'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + a = 2.339370909 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + a = 2.339370909 + 1.3125
a = 2.339370909 + 1.3125

Combine like terms: 2.339370909 + 1.3125 = 3.651870909
a = 3.651870909

Simplifying
a = 3.651870909

Subproblem 2
a + -1.3125 = -2.339370909

Simplifying
a + -1.3125 = -2.339370909

Reorder the terms:
-1.3125 + a = -2.339370909

Solving
-1.3125 + a = -2.339370909

Solving for variable 'a'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + a = -2.339370909 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + a = -2.339370909 + 1.3125
a = -2.339370909 + 1.3125

Combine like terms: -2.339370909 + 1.3125 = -1.026870909
a = -1.026870909

Simplifying
a = -1.026870909

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.651870909, -1.026870909}