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

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

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

Reorder the terms:
8a + -2a(5 + a) = 2(a + -1)
8a + (5 * -2a + a * -2a) = 2(a + -1)
8a + (-10a + -2a2) = 2(a + -1)

Combine like terms: 8a + -10a = -2a
-2a + -2a2 = 2(a + -1)

Reorder the terms:
-2a + -2a2 = 2(-1 + a)
-2a + -2a2 = (-1 * 2 + a * 2)
-2a + -2a2 = (-2 + 2a)

Solving
-2a + -2a2 = -2 + 2a

Solving for variable 'a'.

Reorder the terms:
2 + -2a + -2a + -2a2 = -2 + 2a + 2 + -2a

Combine like terms: -2a + -2a = -4a
2 + -4a + -2a2 = -2 + 2a + 2 + -2a

Reorder the terms:
2 + -4a + -2a2 = -2 + 2 + 2a + -2a

Combine like terms: -2 + 2 = 0
2 + -4a + -2a2 = 0 + 2a + -2a
2 + -4a + -2a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
2 + -4a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2a + -1a2) = 0

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

Simplifying
1 + -2a + -1a2 = 0

Solving
1 + -2a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 2a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 2a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2a + a2 = 0 + 1
2a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
2a + a2 = 1

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 1 + 1

Reorder the terms:
1 + 2a + a2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2a + a2 = 2

Factor a perfect square on the left side:
(a + 1)(a + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(a + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
a + 1 = 1.414213562

Simplifying
a + 1 = 1.414213562

Reorder the terms:
1 + a = 1.414213562

Solving
1 + a = 1.414213562

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + a = 1.414213562 + -1
a = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
a = 0.414213562

Simplifying
a = 0.414213562

Subproblem 2
a + 1 = -1.414213562

Simplifying
a + 1 = -1.414213562

Reorder the terms:
1 + a = -1.414213562

Solving
1 + a = -1.414213562

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + a = -1.414213562 + -1
a = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
a = -2.414213562

Simplifying
a = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.414213562, -2.414213562}
Solution
a = {0.414213562, -2.414213562}