2(9-5)=4a(2a+10)

Solution for 2(9-5)=4a(2a+10) equation:

Simplifying
2(9 + -5) = 4a(2a + 10)

Combine like terms: 9 + -5 = 4
2(4) = 4a(2a + 10)

Multiply 2 * 4
8 = 4a(2a + 10)

Reorder the terms:
8 = 4a(10 + 2a)
8 = (10 * 4a + 2a * 4a)
8 = (40a + 8a2)

Solving
8 = 40a + 8a2

Solving for variable 'a'.

Reorder the terms:
8 + -40a + -8a2 = 40a + -40a + 8a2 + -8a2

Combine like terms: 40a + -40a = 0
8 + -40a + -8a2 = 0 + 8a2 + -8a2
8 + -40a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
8 + -40a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -5a + -1a2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -5a + -1a2)' equal to zero and attempt to solve:

Simplifying
1 + -5a + -1a2 = 0

Solving
1 + -5a + -1a2 = 0

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

Divide each side by '-1'.
-1 + 5a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 5a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5a + a2 = 0 + 1
5a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
5a + a2 = 1

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 1 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 1 + 6.25

Combine like terms: 1 + 6.25 = 7.25
6.25 + 5a + a2 = 7.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(a + 2.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
a + 2.5 = 2.692582404

Simplifying
a + 2.5 = 2.692582404

Reorder the terms:
2.5 + a = 2.692582404

Solving
2.5 + a = 2.692582404

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = 2.692582404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = 2.692582404 + -2.5
a = 2.692582404 + -2.5

Combine like terms: 2.692582404 + -2.5 = 0.192582404
a = 0.192582404

Simplifying
a = 0.192582404

Subproblem 2
a + 2.5 = -2.692582404

Simplifying
a + 2.5 = -2.692582404

Reorder the terms:
2.5 + a = -2.692582404

Solving
2.5 + a = -2.692582404

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = -2.692582404 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = -2.692582404 + -2.5
a = -2.692582404 + -2.5

Combine like terms: -2.692582404 + -2.5 = -5.192582404
a = -5.192582404

Simplifying
a = -5.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.192582404, -5.192582404}
Solution
a = {0.192582404, -5.192582404}