-5a(a+7)=-36-6a

Solution for -5a(a+7)=-36-6a equation:

Simplifying
-5a(a + 7) = -36 + -6a

Reorder the terms:
-5a(7 + a) = -36 + -6a
(7 * -5a + a * -5a) = -36 + -6a
(-35a + -5a2) = -36 + -6a

Solving
-35a + -5a2 = -36 + -6a

Solving for variable 'a'.

Reorder the terms:
36 + -35a + 6a + -5a2 = -36 + -6a + 36 + 6a

Combine like terms: -35a + 6a = -29a
36 + -29a + -5a2 = -36 + -6a + 36 + 6a

Reorder the terms:
36 + -29a + -5a2 = -36 + 36 + -6a + 6a

Combine like terms: -36 + 36 = 0
36 + -29a + -5a2 = 0 + -6a + 6a
36 + -29a + -5a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
36 + -29a + -5a2 = 0

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

Divide each side by '-5'.
-7.2 + 5.8a + a2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + 5.8a + 7.2 + a2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + 5.8a + a2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + 5.8a + a2 = 0 + 7.2
5.8a + a2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
5.8a + a2 = 7.2

The a term is 5.8a.  Take half its coefficient (2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
5.8a + 8.41 + a2 = 7.2 + 8.41

Reorder the terms:
8.41 + 5.8a + a2 = 7.2 + 8.41

Combine like terms: 7.2 + 8.41 = 15.61
8.41 + 5.8a + a2 = 15.61

Factor a perfect square on the left side:
(a + 2.9)(a + 2.9) = 15.61

Calculate the square root of the right side: 3.950949253

Break this problem into two subproblems by setting 
(a + 2.9) equal to 3.950949253 and -3.950949253.

Subproblem 1
a + 2.9 = 3.950949253

Simplifying
a + 2.9 = 3.950949253

Reorder the terms:
2.9 + a = 3.950949253

Solving
2.9 + a = 3.950949253

Solving for variable 'a'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + a = 3.950949253 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + a = 3.950949253 + -2.9
a = 3.950949253 + -2.9

Combine like terms: 3.950949253 + -2.9 = 1.050949253
a = 1.050949253

Simplifying
a = 1.050949253

Subproblem 2
a + 2.9 = -3.950949253

Simplifying
a + 2.9 = -3.950949253

Reorder the terms:
2.9 + a = -3.950949253

Solving
2.9 + a = -3.950949253

Solving for variable 'a'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + a = -3.950949253 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + a = -3.950949253 + -2.9
a = -3.950949253 + -2.9

Combine like terms: -3.950949253 + -2.9 = -6.850949253
a = -6.850949253

Simplifying
a = -6.850949253

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.050949253, -6.850949253}