4a(a+6)=12-36

Solution for 4a(a+6)=12-36 equation:

Simplifying
4a(a + 6) = 12 + -36

Reorder the terms:
4a(6 + a) = 12 + -36
(6 * 4a + a * 4a) = 12 + -36
(24a + 4a2) = 12 + -36

Combine like terms: 12 + -36 = -24
24a + 4a2 = -24

Solving
24a + 4a2 = -24

Solving for variable 'a'.

Reorder the terms:
24 + 24a + 4a2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 24a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 6a + a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + 6a + a2)' equal to zero and attempt to solve:

Simplifying
6 + 6a + a2 = 0

Solving
6 + 6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -6 + 9

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

Combine like terms: -6 + 9 = 3
9 + 6a + a2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + 3) equal to 1.732050808 and -1.732050808.

Subproblem 1
a + 3 = 1.732050808

Simplifying
a + 3 = 1.732050808

Reorder the terms:
3 + a = 1.732050808

Solving
3 + a = 1.732050808

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 = 1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + a = 1.732050808 + -3
a = 1.732050808 + -3

Combine like terms: 1.732050808 + -3 = -1.267949192
a = -1.267949192

Simplifying
a = -1.267949192

Subproblem 2
a + 3 = -1.732050808

Simplifying
a + 3 = -1.732050808

Reorder the terms:
3 + a = -1.732050808

Solving
3 + a = -1.732050808

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 = -1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + a = -1.732050808 + -3
a = -1.732050808 + -3

Combine like terms: -1.732050808 + -3 = -4.732050808
a = -4.732050808

Simplifying
a = -4.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.267949192, -4.732050808}
Solution
a = {-1.267949192, -4.732050808}