x-([29-2x]*(76x-45))=49273738

Solution for x-([29-2x]*(76x-45))=49273738 equation:

Simplifying
x + -1([29 + -2x](76x + -45)) = 49273738

Reorder the terms:
x + -1([29 + -2x](-45 + 76x)) = 49273738

Multiply [29 + -2x] * (-45 + 76x)
x + -1([29(-45 + 76x) + -2x * (-45 + 76x)]) = 49273738
x + -1([(-45 * 29 + 76x * 29) + -2x * (-45 + 76x)]) = 49273738
x + -1([(-1305 + 2204x) + -2x * (-45 + 76x)]) = 49273738
x + -1([-1305 + 2204x + (-45 * -2x + 76x * -2x)]) = 49273738
x + -1([-1305 + 2204x + (90x + -152x2)]) = 49273738

Combine like terms: 2204x + 90x = 2294x
x + -1([-1305 + 2294x + -152x2]) = 49273738
x + (-1305 * -1 + 2294x * -1 + -152x2 * -1) = 49273738
x + (1305 + -2294x + 152x2) = 49273738

Reorder the terms:
1305 + x + -2294x + 152x2 = 49273738

Combine like terms: x + -2294x = -2293x
1305 + -2293x + 152x2 = 49273738

Solving
1305 + -2293x + 152x2 = 49273738

Solving for variable 'x'.

Reorder the terms:
1305 + -49273738 + -2293x + 152x2 = 49273738 + -49273738

Combine like terms: 1305 + -49273738 = -49272433
-49272433 + -2293x + 152x2 = 49273738 + -49273738

Combine like terms: 49273738 + -49273738 = 0
-49272433 + -2293x + 152x2 = 0

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

Divide each side by '152'.
-324160.7434 + -15.08552632x + x2 = 0

Move the constant term to the right:

Add '324160.7434' to each side of the equation.
-324160.7434 + -15.08552632x + 324160.7434 + x2 = 0 + 324160.7434

Reorder the terms:
-324160.7434 + 324160.7434 + -15.08552632x + x2 = 0 + 324160.7434

Combine like terms: -324160.7434 + 324160.7434 = 0.0000
0.0000 + -15.08552632x + x2 = 0 + 324160.7434
-15.08552632x + x2 = 0 + 324160.7434

Combine like terms: 0 + 324160.7434 = 324160.7434
-15.08552632x + x2 = 324160.7434

The x term is -15.08552632x.  Take half its coefficient (-7.54276316).
Square it (56.89327609) and add it to both sides.

Add '56.89327609' to each side of the equation.
-15.08552632x + 56.89327609 + x2 = 324160.7434 + 56.89327609

Reorder the terms:
56.89327609 + -15.08552632x + x2 = 324160.7434 + 56.89327609

Combine like terms: 324160.7434 + 56.89327609 = 324217.63667609
56.89327609 + -15.08552632x + x2 = 324217.63667609

Factor a perfect square on the left side:
(x + -7.54276316)(x + -7.54276316) = 324217.63667609

Calculate the square root of the right side: 569.40112107

Break this problem into two subproblems by setting 
(x + -7.54276316) equal to 569.40112107 and -569.40112107.

Subproblem 1
x + -7.54276316 = 569.40112107

Simplifying
x + -7.54276316 = 569.40112107

Reorder the terms:
-7.54276316 + x = 569.40112107

Solving
-7.54276316 + x = 569.40112107

Solving for variable 'x'.

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

Add '7.54276316' to each side of the equation.
-7.54276316 + 7.54276316 + x = 569.40112107 + 7.54276316

Combine like terms: -7.54276316 + 7.54276316 = 0.00000000
0.00000000 + x = 569.40112107 + 7.54276316
x = 569.40112107 + 7.54276316

Combine like terms: 569.40112107 + 7.54276316 = 576.94388423
x = 576.94388423

Simplifying
x = 576.94388423

Subproblem 2
x + -7.54276316 = -569.40112107

Simplifying
x + -7.54276316 = -569.40112107

Reorder the terms:
-7.54276316 + x = -569.40112107

Solving
-7.54276316 + x = -569.40112107

Solving for variable 'x'.

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

Add '7.54276316' to each side of the equation.
-7.54276316 + 7.54276316 + x = -569.40112107 + 7.54276316

Combine like terms: -7.54276316 + 7.54276316 = 0.00000000
0.00000000 + x = -569.40112107 + 7.54276316
x = -569.40112107 + 7.54276316

Combine like terms: -569.40112107 + 7.54276316 = -561.85835791
x = -561.85835791

Simplifying
x = -561.85835791

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {576.94388423, -561.85835791}