4a-2a(a+9)=6

Solution for 4a-2a(a+9)=6 equation:

Simplifying
4a + -2a(a + 9) = 6

Reorder the terms:
4a + -2a(9 + a) = 6
4a + (9 * -2a + a * -2a) = 6
4a + (-18a + -2a2) = 6

Combine like terms: 4a + -18a = -14a
-14a + -2a2 = 6

Solving
-14a + -2a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + -14a + -2a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -14a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 7a + a2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 7a + a2)' equal to zero and attempt to solve:

Simplifying
3 + 7a + a2 = 0

Solving
3 + 7a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + 7a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7a + a2 = 0 + -3
7a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
7a + a2 = -3

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 = -3 + 12.25

Reorder the terms:
12.25 + 7a + a2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7a + a2 = 9.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(a + 3.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
a + 3.5 = 3.041381265

Simplifying
a + 3.5 = 3.041381265

Reorder the terms:
3.5 + a = 3.041381265

Solving
3.5 + a = 3.041381265

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 = 3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 3.041381265 + -3.5
a = 3.041381265 + -3.5

Combine like terms: 3.041381265 + -3.5 = -0.458618735
a = -0.458618735

Simplifying
a = -0.458618735

Subproblem 2
a + 3.5 = -3.041381265

Simplifying
a + 3.5 = -3.041381265

Reorder the terms:
3.5 + a = -3.041381265

Solving
3.5 + a = -3.041381265

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 = -3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -3.041381265 + -3.5
a = -3.041381265 + -3.5

Combine like terms: -3.041381265 + -3.5 = -6.541381265
a = -6.541381265

Simplifying
a = -6.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.458618735, -6.541381265}
Solution
a = {-0.458618735, -6.541381265}