5a(8-a)=4a-10

Solution for 5a(8-a)=4a-10 equation:

Simplifying
5a(8 + -1a) = 4a + -10
(8 * 5a + -1a * 5a) = 4a + -10
(40a + -5a2) = 4a + -10

Reorder the terms:
40a + -5a2 = -10 + 4a

Solving
40a + -5a2 = -10 + 4a

Solving for variable 'a'.

Reorder the terms:
10 + 40a + -4a + -5a2 = -10 + 4a + 10 + -4a

Combine like terms: 40a + -4a = 36a
10 + 36a + -5a2 = -10 + 4a + 10 + -4a

Reorder the terms:
10 + 36a + -5a2 = -10 + 10 + 4a + -4a

Combine like terms: -10 + 10 = 0
10 + 36a + -5a2 = 0 + 4a + -4a
10 + 36a + -5a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
10 + 36a + -5a2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2 + -7.2a + a2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7.2a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + -7.2a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7.2a + a2 = 0 + 2
-7.2a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7.2a + a2 = 2

The a term is -7.2a.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2a + 12.96 + a2 = 2 + 12.96

Reorder the terms:
12.96 + -7.2a + a2 = 2 + 12.96

Combine like terms: 2 + 12.96 = 14.96
12.96 + -7.2a + a2 = 14.96

Factor a perfect square on the left side:
(a + -3.6)(a + -3.6) = 14.96

Calculate the square root of the right side: 3.867815921

Break this problem into two subproblems by setting 
(a + -3.6) equal to 3.867815921 and -3.867815921.

Subproblem 1
a + -3.6 = 3.867815921

Simplifying
a + -3.6 = 3.867815921

Reorder the terms:
-3.6 + a = 3.867815921

Solving
-3.6 + a = 3.867815921

Solving for variable 'a'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + a = 3.867815921 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + a = 3.867815921 + 3.6
a = 3.867815921 + 3.6

Combine like terms: 3.867815921 + 3.6 = 7.467815921
a = 7.467815921

Simplifying
a = 7.467815921

Subproblem 2
a + -3.6 = -3.867815921

Simplifying
a + -3.6 = -3.867815921

Reorder the terms:
-3.6 + a = -3.867815921

Solving
-3.6 + a = -3.867815921

Solving for variable 'a'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + a = -3.867815921 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + a = -3.867815921 + 3.6
a = -3.867815921 + 3.6

Combine like terms: -3.867815921 + 3.6 = -0.267815921
a = -0.267815921

Simplifying
a = -0.267815921

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.467815921, -0.267815921}