73=3(6a+6)7a

Solution for 73=3(6a+6)7a equation:

Simplifying
73 = 3(6a + 6) * 7a

Reorder the terms:
73 = 3(6 + 6a) * 7a

Reorder the terms for easier multiplication:
73 = 3 * 7a(6 + 6a)

Multiply 3 * 7
73 = 21a(6 + 6a)
73 = (6 * 21a + 6a * 21a)
73 = (126a + 126a2)

Solving
73 = 126a + 126a2

Solving for variable 'a'.

Reorder the terms:
73 + -126a + -126a2 = 126a + -126a + 126a2 + -126a2

Combine like terms: 126a + -126a = 0
73 + -126a + -126a2 = 0 + 126a2 + -126a2
73 + -126a + -126a2 = 126a2 + -126a2

Combine like terms: 126a2 + -126a2 = 0
73 + -126a + -126a2 = 0

Begin completing the square.  Divide all terms by
-126 the coefficient of the squared term: 

Divide each side by '-126'.
-0.5793650794 + a + a2 = 0

Move the constant term to the right:

Add '0.5793650794' to each side of the equation.
-0.5793650794 + a + 0.5793650794 + a2 = 0 + 0.5793650794

Reorder the terms:
-0.5793650794 + 0.5793650794 + a + a2 = 0 + 0.5793650794

Combine like terms: -0.5793650794 + 0.5793650794 = 0.0000000000
0.0000000000 + a + a2 = 0 + 0.5793650794
a + a2 = 0 + 0.5793650794

Combine like terms: 0 + 0.5793650794 = 0.5793650794
a + a2 = 0.5793650794

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = 0.5793650794 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = 0.5793650794 + 0.25

Combine like terms: 0.5793650794 + 0.25 = 0.8293650794
1.25 + a2 = 0.8293650794

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.8293650794

Calculate the square root of the right side: 0.910694833

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.910694833 and -0.910694833.

Subproblem 1
a + 0.5 = 0.910694833

Simplifying
a + 0.5 = 0.910694833

Reorder the terms:
0.5 + a = 0.910694833

Solving
0.5 + a = 0.910694833

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 0.910694833 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 0.910694833 + -0.5
a = 0.910694833 + -0.5

Combine like terms: 0.910694833 + -0.5 = 0.410694833
a = 0.410694833

Simplifying
a = 0.410694833

Subproblem 2
a + 0.5 = -0.910694833

Simplifying
a + 0.5 = -0.910694833

Reorder the terms:
0.5 + a = -0.910694833

Solving
0.5 + a = -0.910694833

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -0.910694833 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -0.910694833 + -0.5
a = -0.910694833 + -0.5

Combine like terms: -0.910694833 + -0.5 = -1.410694833
a = -1.410694833

Simplifying
a = -1.410694833

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.410694833, -1.410694833}