5*(a-4)*8a=55

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Solution for 5*(a-4)*8a=55 equation: 


Simplifying
5(a + -4) * 8a = 55

Reorder the terms:
5(-4 + a) * 8a = 55

Reorder the terms for easier multiplication:
5 * 8a(-4 + a) = 55

Multiply 5 * 8
40a(-4 + a) = 55
(-4 * 40a + a * 40a) = 55
(-160a + 40a2) = 55

Solving
-160a + 40a2 = 55

Solving for variable 'a'.

Reorder the terms:
-55 + -160a + 40a2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + -160a + 40a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + -32a + 8a2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-11 + -32a + 8a2)' equal to zero and attempt to solve:

Simplifying
-11 + -32a + 8a2 = 0

Solving
-11 + -32a + 8a2 = 0

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

Divide each side by '8'.
-1.375 + -4a + a2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + -4a + 1.375 + a2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + -4a + a2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + -4a + a2 = 0 + 1.375
-4a + a2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
-4a + a2 = 1.375

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 1.375 + 4

Reorder the terms:
4 + -4a + a2 = 1.375 + 4

Combine like terms: 1.375 + 4 = 5.375
4 + -4a + a2 = 5.375

Factor a perfect square on the left side:
(a + -2)(a + -2) = 5.375

Calculate the square root of the right side: 2.318404624

Break this problem into two subproblems by setting 
(a + -2) equal to 2.318404624 and -2.318404624.


Subproblem 1
a + -2 = 2.318404624

Simplifying
a + -2 = 2.318404624

Reorder the terms:
-2 + a = 2.318404624

Solving
-2 + a = 2.318404624

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = 2.318404624 + 2

Combine like terms: -2 + 2 = 0
0 + a = 2.318404624 + 2
a = 2.318404624 + 2

Combine like terms: 2.318404624 + 2 = 4.318404624
a = 4.318404624

Simplifying
a = 4.318404624


Subproblem 2
a + -2 = -2.318404624

Simplifying
a + -2 = -2.318404624

Reorder the terms:
-2 + a = -2.318404624

Solving
-2 + a = -2.318404624

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 2 + a = -2.318404624 + 2

Combine like terms: -2 + 2 = 0
0 + a = -2.318404624 + 2
a = -2.318404624 + 2

Combine like terms: -2.318404624 + 2 = -0.318404624
a = -0.318404624

Simplifying
a = -0.318404624


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.318404624, -0.318404624}
Solution
a = {4.318404624, -0.318404624}

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