5[2a(6-a)+2(a-4)+5]=0

Solution for 5[2a(6-a)+2(a-4)+5]=0 equation:

Simplifying
5[2a(6 + -1a) + 2(a + -4) + 5] = 0
5[(6 * 2a + -1a * 2a) + 2(a + -4) + 5] = 0
5[(12a + -2a2) + 2(a + -4) + 5] = 0

Reorder the terms:
5[12a + -2a2 + 2(-4 + a) + 5] = 0
5[12a + -2a2 + (-4 * 2 + a * 2) + 5] = 0
5[12a + -2a2 + (-8 + 2a) + 5] = 0

Reorder the terms:
5[-8 + 5 + 12a + 2a + -2a2] = 0

Combine like terms: -8 + 5 = -3
5[-3 + 12a + 2a + -2a2] = 0

Combine like terms: 12a + 2a = 14a
5[-3 + 14a + -2a2] = 0
[-3 * 5 + 14a * 5 + -2a2 * 5] = 0
[-15 + 70a + -10a2] = 0

Solving
-15 + 70a + -10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 14a + -2a2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + 14a + -2a2)' equal to zero and attempt to solve:

Simplifying
-3 + 14a + -2a2 = 0

Solving
-3 + 14a + -2a2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -7a + a2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -7a + -1.5 + a2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -7a + a2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -7a + a2 = 0 + -1.5
-7a + a2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-7a + a2 = -1.5

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = -1.5 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -1.5 + 12.25

Combine like terms: -1.5 + 12.25 = 10.75
12.25 + -7a + a2 = 10.75

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 10.75

Calculate the square root of the right side: 3.278719262

Break this problem into two subproblems by setting 
(a + -3.5) equal to 3.278719262 and -3.278719262.

Subproblem 1
a + -3.5 = 3.278719262

Simplifying
a + -3.5 = 3.278719262

Reorder the terms:
-3.5 + a = 3.278719262

Solving
-3.5 + a = 3.278719262

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = 3.278719262 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 3.278719262 + 3.5
a = 3.278719262 + 3.5

Combine like terms: 3.278719262 + 3.5 = 6.778719262
a = 6.778719262

Simplifying
a = 6.778719262

Subproblem 2
a + -3.5 = -3.278719262

Simplifying
a + -3.5 = -3.278719262

Reorder the terms:
-3.5 + a = -3.278719262

Solving
-3.5 + a = -3.278719262

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = -3.278719262 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -3.278719262 + 3.5
a = -3.278719262 + 3.5

Combine like terms: -3.278719262 + 3.5 = 0.221280738
a = 0.221280738

Simplifying
a = 0.221280738

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.778719262, 0.221280738}
Solution
a = {6.778719262, 0.221280738}