6x(9x+4)+9=167-4(7x+3)

Solution for 6x(9x+4)+9=167-4(7x+3) equation:

Simplifying
6x(9x + 4) + 9 = 167 + -4(7x + 3)

Reorder the terms:
6x(4 + 9x) + 9 = 167 + -4(7x + 3)
(4 * 6x + 9x * 6x) + 9 = 167 + -4(7x + 3)
(24x + 54x2) + 9 = 167 + -4(7x + 3)

Reorder the terms:
9 + 24x + 54x2 = 167 + -4(7x + 3)

Reorder the terms:
9 + 24x + 54x2 = 167 + -4(3 + 7x)
9 + 24x + 54x2 = 167 + (3 * -4 + 7x * -4)
9 + 24x + 54x2 = 167 + (-12 + -28x)

Combine like terms: 167 + -12 = 155
9 + 24x + 54x2 = 155 + -28x

Solving
9 + 24x + 54x2 = 155 + -28x

Solving for variable 'x'.

Reorder the terms:
9 + -155 + 24x + 28x + 54x2 = 155 + -28x + -155 + 28x

Combine like terms: 9 + -155 = -146
-146 + 24x + 28x + 54x2 = 155 + -28x + -155 + 28x

Combine like terms: 24x + 28x = 52x
-146 + 52x + 54x2 = 155 + -28x + -155 + 28x

Reorder the terms:
-146 + 52x + 54x2 = 155 + -155 + -28x + 28x

Combine like terms: 155 + -155 = 0
-146 + 52x + 54x2 = 0 + -28x + 28x
-146 + 52x + 54x2 = -28x + 28x

Combine like terms: -28x + 28x = 0
-146 + 52x + 54x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-73 + 26x + 27x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-73 + 26x + 27x2)' equal to zero and attempt to solve:

Simplifying
-73 + 26x + 27x2 = 0

Solving
-73 + 26x + 27x2 = 0

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

Divide each side by '27'.
-2.703703704 + 0.962962963x + x2 = 0

Move the constant term to the right:

Add '2.703703704' to each side of the equation.
-2.703703704 + 0.962962963x + 2.703703704 + x2 = 0 + 2.703703704

Reorder the terms:
-2.703703704 + 2.703703704 + 0.962962963x + x2 = 0 + 2.703703704

Combine like terms: -2.703703704 + 2.703703704 = 0.000000000
0.000000000 + 0.962962963x + x2 = 0 + 2.703703704
0.962962963x + x2 = 0 + 2.703703704

Combine like terms: 0 + 2.703703704 = 2.703703704
0.962962963x + x2 = 2.703703704

The x term is 0.962962963x.  Take half its coefficient (0.4814814815).
Square it (0.2318244170) and add it to both sides.

Add '0.2318244170' to each side of the equation.
0.962962963x + 0.2318244170 + x2 = 2.703703704 + 0.2318244170

Reorder the terms:
0.2318244170 + 0.962962963x + x2 = 2.703703704 + 0.2318244170

Combine like terms: 2.703703704 + 0.2318244170 = 2.935528121
0.2318244170 + 0.962962963x + x2 = 2.935528121

Factor a perfect square on the left side:
(x + 0.4814814815)(x + 0.4814814815) = 2.935528121

Calculate the square root of the right side: 1.713338297

Break this problem into two subproblems by setting 
(x + 0.4814814815) equal to 1.713338297 and -1.713338297.

Subproblem 1
x + 0.4814814815 = 1.713338297

Simplifying
x + 0.4814814815 = 1.713338297

Reorder the terms:
0.4814814815 + x = 1.713338297

Solving
0.4814814815 + x = 1.713338297

Solving for variable 'x'.

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

Add '-0.4814814815' to each side of the equation.
0.4814814815 + -0.4814814815 + x = 1.713338297 + -0.4814814815

Combine like terms: 0.4814814815 + -0.4814814815 = 0.0000000000
0.0000000000 + x = 1.713338297 + -0.4814814815
x = 1.713338297 + -0.4814814815

Combine like terms: 1.713338297 + -0.4814814815 = 1.2318568155
x = 1.2318568155

Simplifying
x = 1.2318568155

Subproblem 2
x + 0.4814814815 = -1.713338297

Simplifying
x + 0.4814814815 = -1.713338297

Reorder the terms:
0.4814814815 + x = -1.713338297

Solving
0.4814814815 + x = -1.713338297

Solving for variable 'x'.

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

Add '-0.4814814815' to each side of the equation.
0.4814814815 + -0.4814814815 + x = -1.713338297 + -0.4814814815

Combine like terms: 0.4814814815 + -0.4814814815 = 0.0000000000
0.0000000000 + x = -1.713338297 + -0.4814814815
x = -1.713338297 + -0.4814814815

Combine like terms: -1.713338297 + -0.4814814815 = -2.1948197785
x = -2.1948197785

Simplifying
x = -2.1948197785

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2318568155, -2.1948197785}
Solution
x = {1.2318568155, -2.1948197785}