2a+5(a+3)+9-a(a+1)=

Solution for 2a+5(a+3)+9-a(a+1)= equation:

Simplifying
2a + 5(a + 3) + 9 + -1a(a + 1) = 0

Reorder the terms:
2a + 5(3 + a) + 9 + -1a(a + 1) = 0
2a + (3 * 5 + a * 5) + 9 + -1a(a + 1) = 0
2a + (15 + 5a) + 9 + -1a(a + 1) = 0

Reorder the terms:
2a + 15 + 5a + 9 + -1a(1 + a) = 0
2a + 15 + 5a + 9 + (1 * -1a + a * -1a) = 0
2a + 15 + 5a + 9 + (-1a + -1a2) = 0

Reorder the terms:
15 + 9 + 2a + 5a + -1a + -1a2 = 0

Combine like terms: 15 + 9 = 24
24 + 2a + 5a + -1a + -1a2 = 0

Combine like terms: 2a + 5a = 7a
24 + 7a + -1a + -1a2 = 0

Combine like terms: 7a + -1a = 6a
24 + 6a + -1a2 = 0

Solving
24 + 6a + -1a2 = 0

Solving for variable 'a'.

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

Divide each side by '-1'.
-24 + -6a + a2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -6a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + -6a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -6a + a2 = 0 + 24
-6a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
-6a + a2 = 24

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = 24 + 9

Reorder the terms:
9 + -6a + a2 = 24 + 9

Combine like terms: 24 + 9 = 33
9 + -6a + a2 = 33

Factor a perfect square on the left side:
(a + -3)(a + -3) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(a + -3) equal to 5.744562647 and -5.744562647.

Subproblem 1
a + -3 = 5.744562647

Simplifying
a + -3 = 5.744562647

Reorder the terms:
-3 + a = 5.744562647

Solving
-3 + a = 5.744562647

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = 5.744562647 + 3

Combine like terms: -3 + 3 = 0
0 + a = 5.744562647 + 3
a = 5.744562647 + 3

Combine like terms: 5.744562647 + 3 = 8.744562647
a = 8.744562647

Simplifying
a = 8.744562647

Subproblem 2
a + -3 = -5.744562647

Simplifying
a + -3 = -5.744562647

Reorder the terms:
-3 + a = -5.744562647

Solving
-3 + a = -5.744562647

Solving for variable 'a'.

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

Add '3' to each side of the equation.
-3 + 3 + a = -5.744562647 + 3

Combine like terms: -3 + 3 = 0
0 + a = -5.744562647 + 3
a = -5.744562647 + 3

Combine like terms: -5.744562647 + 3 = -2.744562647
a = -2.744562647

Simplifying
a = -2.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.744562647, -2.744562647}