12.6*(3x-8)=17x(24x+72)

Solution for 12.6*(3x-8)=17x(24x+72) equation:

Simplifying
12.6(3x + -8) = 17x(24x + 72)

Reorder the terms:
12.6(-8 + 3x) = 17x(24x + 72)
(-8 * 12.6 + 3x * 12.6) = 17x(24x + 72)
(-100.8 + 37.8x) = 17x(24x + 72)

Reorder the terms:
-100.8 + 37.8x = 17x(72 + 24x)
-100.8 + 37.8x = (72 * 17x + 24x * 17x)
-100.8 + 37.8x = (1224x + 408x2)

Solving
-100.8 + 37.8x = 1224x + 408x2

Solving for variable 'x'.

Combine like terms: 37.8x + -1224x = -1186.2x
-100.8 + -1186.2x + -408x2 = 1224x + 408x2 + -1224x + -408x2

Reorder the terms:
-100.8 + -1186.2x + -408x2 = 1224x + -1224x + 408x2 + -408x2

Combine like terms: 1224x + -1224x = 0
-100.8 + -1186.2x + -408x2 = 0 + 408x2 + -408x2
-100.8 + -1186.2x + -408x2 = 408x2 + -408x2

Combine like terms: 408x2 + -408x2 = 0
-100.8 + -1186.2x + -408x2 = 0

Begin completing the square.  Divide all terms by
-408 the coefficient of the squared term: 

Divide each side by '-408'.
0.2470588235 + 2.907352941x + x2 = 0

Move the constant term to the right:

Add '-0.2470588235' to each side of the equation.
0.2470588235 + 2.907352941x + -0.2470588235 + x2 = 0 + -0.2470588235

Reorder the terms:
0.2470588235 + -0.2470588235 + 2.907352941x + x2 = 0 + -0.2470588235

Combine like terms: 0.2470588235 + -0.2470588235 = 0.0000000000
0.0000000000 + 2.907352941x + x2 = 0 + -0.2470588235
2.907352941x + x2 = 0 + -0.2470588235

Combine like terms: 0 + -0.2470588235 = -0.2470588235
2.907352941x + x2 = -0.2470588235

The x term is 2.907352941x.  Take half its coefficient (1.453676471).
Square it (2.113175282) and add it to both sides.

Add '2.113175282' to each side of the equation.
2.907352941x + 2.113175282 + x2 = -0.2470588235 + 2.113175282

Reorder the terms:
2.113175282 + 2.907352941x + x2 = -0.2470588235 + 2.113175282

Combine like terms: -0.2470588235 + 2.113175282 = 1.8661164585
2.113175282 + 2.907352941x + x2 = 1.8661164585

Factor a perfect square on the left side:
(x + 1.453676471)(x + 1.453676471) = 1.8661164585

Calculate the square root of the right side: 1.366058732

Break this problem into two subproblems by setting 
(x + 1.453676471) equal to 1.366058732 and -1.366058732.

Subproblem 1
x + 1.453676471 = 1.366058732

Simplifying
x + 1.453676471 = 1.366058732

Reorder the terms:
1.453676471 + x = 1.366058732

Solving
1.453676471 + x = 1.366058732

Solving for variable 'x'.

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

Add '-1.453676471' to each side of the equation.
1.453676471 + -1.453676471 + x = 1.366058732 + -1.453676471

Combine like terms: 1.453676471 + -1.453676471 = 0.000000000
0.000000000 + x = 1.366058732 + -1.453676471
x = 1.366058732 + -1.453676471

Combine like terms: 1.366058732 + -1.453676471 = -0.087617739
x = -0.087617739

Simplifying
x = -0.087617739

Subproblem 2
x + 1.453676471 = -1.366058732

Simplifying
x + 1.453676471 = -1.366058732

Reorder the terms:
1.453676471 + x = -1.366058732

Solving
1.453676471 + x = -1.366058732

Solving for variable 'x'.

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

Add '-1.453676471' to each side of the equation.
1.453676471 + -1.453676471 + x = -1.366058732 + -1.453676471

Combine like terms: 1.453676471 + -1.453676471 = 0.000000000
0.000000000 + x = -1.366058732 + -1.453676471
x = -1.366058732 + -1.453676471

Combine like terms: -1.366058732 + -1.453676471 = -2.819735203
x = -2.819735203

Simplifying
x = -2.819735203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.087617739, -2.819735203}