33a(3+7a)=7(3a+2)

Solution for 33a(3+7a)=7(3a+2) equation:

Simplifying
33a(3 + 7a) = 7(3a + 2)
(3 * 33a + 7a * 33a) = 7(3a + 2)
(99a + 231a2) = 7(3a + 2)

Reorder the terms:
99a + 231a2 = 7(2 + 3a)
99a + 231a2 = (2 * 7 + 3a * 7)
99a + 231a2 = (14 + 21a)

Solving
99a + 231a2 = 14 + 21a

Solving for variable 'a'.

Reorder the terms:
-14 + 99a + -21a + 231a2 = 14 + 21a + -14 + -21a

Combine like terms: 99a + -21a = 78a
-14 + 78a + 231a2 = 14 + 21a + -14 + -21a

Reorder the terms:
-14 + 78a + 231a2 = 14 + -14 + 21a + -21a

Combine like terms: 14 + -14 = 0
-14 + 78a + 231a2 = 0 + 21a + -21a
-14 + 78a + 231a2 = 21a + -21a

Combine like terms: 21a + -21a = 0
-14 + 78a + 231a2 = 0

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

Divide each side by '231'.
-0.06060606061 + 0.3376623377a + a2 = 0

Move the constant term to the right:

Add '0.06060606061' to each side of the equation.
-0.06060606061 + 0.3376623377a + 0.06060606061 + a2 = 0 + 0.06060606061

Reorder the terms:
-0.06060606061 + 0.06060606061 + 0.3376623377a + a2 = 0 + 0.06060606061

Combine like terms: -0.06060606061 + 0.06060606061 = 0.00000000000
0.00000000000 + 0.3376623377a + a2 = 0 + 0.06060606061
0.3376623377a + a2 = 0 + 0.06060606061

Combine like terms: 0 + 0.06060606061 = 0.06060606061
0.3376623377a + a2 = 0.06060606061

The a term is 0.3376623377a.  Take half its coefficient (0.1688311689).
Square it (0.02850396359) and add it to both sides.

Add '0.02850396359' to each side of the equation.
0.3376623377a + 0.02850396359 + a2 = 0.06060606061 + 0.02850396359

Reorder the terms:
0.02850396359 + 0.3376623377a + a2 = 0.06060606061 + 0.02850396359

Combine like terms: 0.06060606061 + 0.02850396359 = 0.0891100242
0.02850396359 + 0.3376623377a + a2 = 0.0891100242

Factor a perfect square on the left side:
(a + 0.1688311689)(a + 0.1688311689) = 0.0891100242

Calculate the square root of the right side: 0.298513022

Break this problem into two subproblems by setting 
(a + 0.1688311689) equal to 0.298513022 and -0.298513022.

Subproblem 1
a + 0.1688311689 = 0.298513022

Simplifying
a + 0.1688311689 = 0.298513022

Reorder the terms:
0.1688311689 + a = 0.298513022

Solving
0.1688311689 + a = 0.298513022

Solving for variable 'a'.

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

Add '-0.1688311689' to each side of the equation.
0.1688311689 + -0.1688311689 + a = 0.298513022 + -0.1688311689

Combine like terms: 0.1688311689 + -0.1688311689 = 0.0000000000
0.0000000000 + a = 0.298513022 + -0.1688311689
a = 0.298513022 + -0.1688311689

Combine like terms: 0.298513022 + -0.1688311689 = 0.1296818531
a = 0.1296818531

Simplifying
a = 0.1296818531

Subproblem 2
a + 0.1688311689 = -0.298513022

Simplifying
a + 0.1688311689 = -0.298513022

Reorder the terms:
0.1688311689 + a = -0.298513022

Solving
0.1688311689 + a = -0.298513022

Solving for variable 'a'.

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

Add '-0.1688311689' to each side of the equation.
0.1688311689 + -0.1688311689 + a = -0.298513022 + -0.1688311689

Combine like terms: 0.1688311689 + -0.1688311689 = 0.0000000000
0.0000000000 + a = -0.298513022 + -0.1688311689
a = -0.298513022 + -0.1688311689

Combine like terms: -0.298513022 + -0.1688311689 = -0.4673441909
a = -0.4673441909

Simplifying
a = -0.4673441909

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.1296818531, -0.4673441909}