2x(9x+8)=(5-2x)-3(2x-3)+29

Solution for 2x(9x+8)=(5-2x)-3(2x-3)+29 equation:

Simplifying
2x(9x + 8) = (5 + -2x) + -3(2x + -3) + 29

Reorder the terms:
2x(8 + 9x) = (5 + -2x) + -3(2x + -3) + 29
(8 * 2x + 9x * 2x) = (5 + -2x) + -3(2x + -3) + 29
(16x + 18x2) = (5 + -2x) + -3(2x + -3) + 29

Remove parenthesis around (5 + -2x)
16x + 18x2 = 5 + -2x + -3(2x + -3) + 29

Reorder the terms:
16x + 18x2 = 5 + -2x + -3(-3 + 2x) + 29
16x + 18x2 = 5 + -2x + (-3 * -3 + 2x * -3) + 29
16x + 18x2 = 5 + -2x + (9 + -6x) + 29

Reorder the terms:
16x + 18x2 = 5 + 9 + 29 + -2x + -6x

Combine like terms: 5 + 9 = 14
16x + 18x2 = 14 + 29 + -2x + -6x

Combine like terms: 14 + 29 = 43
16x + 18x2 = 43 + -2x + -6x

Combine like terms: -2x + -6x = -8x
16x + 18x2 = 43 + -8x

Solving
16x + 18x2 = 43 + -8x

Solving for variable 'x'.

Reorder the terms:
-43 + 16x + 8x + 18x2 = 43 + -8x + -43 + 8x

Combine like terms: 16x + 8x = 24x
-43 + 24x + 18x2 = 43 + -8x + -43 + 8x

Reorder the terms:
-43 + 24x + 18x2 = 43 + -43 + -8x + 8x

Combine like terms: 43 + -43 = 0
-43 + 24x + 18x2 = 0 + -8x + 8x
-43 + 24x + 18x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-43 + 24x + 18x2 = 0

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

Divide each side by '18'.
-2.388888889 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '2.388888889' to each side of the equation.
-2.388888889 + 1.333333333x + 2.388888889 + x2 = 0 + 2.388888889

Reorder the terms:
-2.388888889 + 2.388888889 + 1.333333333x + x2 = 0 + 2.388888889

Combine like terms: -2.388888889 + 2.388888889 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 2.388888889
1.333333333x + x2 = 0 + 2.388888889

Combine like terms: 0 + 2.388888889 = 2.388888889
1.333333333x + x2 = 2.388888889

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 2.388888889 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 2.388888889 + 0.4444444442

Combine like terms: 2.388888889 + 0.4444444442 = 2.8333333332
0.4444444442 + 1.333333333x + x2 = 2.8333333332

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 2.8333333332

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.683250823 and -1.683250823.

Subproblem 1
x + 0.6666666665 = 1.683250823

Simplifying
x + 0.6666666665 = 1.683250823

Reorder the terms:
0.6666666665 + x = 1.683250823

Solving
0.6666666665 + x = 1.683250823

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.683250823 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.683250823 + -0.6666666665
x = 1.683250823 + -0.6666666665

Combine like terms: 1.683250823 + -0.6666666665 = 1.0165841565
x = 1.0165841565

Simplifying
x = 1.0165841565

Subproblem 2
x + 0.6666666665 = -1.683250823

Simplifying
x + 0.6666666665 = -1.683250823

Reorder the terms:
0.6666666665 + x = -1.683250823

Solving
0.6666666665 + x = -1.683250823

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.683250823 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.683250823 + -0.6666666665
x = -1.683250823 + -0.6666666665

Combine like terms: -1.683250823 + -0.6666666665 = -2.3499174895
x = -2.3499174895

Simplifying
x = -2.3499174895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0165841565, -2.3499174895}