x-([29-2x]*(76x-45))=3x

Solution for x-([29-2x]*(76x-45))=3x equation:

Simplifying
x + -1([29 + -2x](76x + -45)) = 3x

Reorder the terms:
x + -1([29 + -2x](-45 + 76x)) = 3x

Multiply [29 + -2x] * (-45 + 76x)
x + -1([29(-45 + 76x) + -2x * (-45 + 76x)]) = 3x
x + -1([(-45 * 29 + 76x * 29) + -2x * (-45 + 76x)]) = 3x
x + -1([(-1305 + 2204x) + -2x * (-45 + 76x)]) = 3x
x + -1([-1305 + 2204x + (-45 * -2x + 76x * -2x)]) = 3x
x + -1([-1305 + 2204x + (90x + -152x2)]) = 3x

Combine like terms: 2204x + 90x = 2294x
x + -1([-1305 + 2294x + -152x2]) = 3x
x + (-1305 * -1 + 2294x * -1 + -152x2 * -1) = 3x
x + (1305 + -2294x + 152x2) = 3x

Reorder the terms:
1305 + x + -2294x + 152x2 = 3x

Combine like terms: x + -2294x = -2293x
1305 + -2293x + 152x2 = 3x

Solving
1305 + -2293x + 152x2 = 3x

Solving for variable 'x'.

Reorder the terms:
1305 + -2293x + -3x + 152x2 = 3x + -3x

Combine like terms: -2293x + -3x = -2296x
1305 + -2296x + 152x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
1305 + -2296x + 152x2 = 0

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

Divide each side by '152'.
8.585526316 + -15.10526316x + x2 = 0

Move the constant term to the right:

Add '-8.585526316' to each side of the equation.
8.585526316 + -15.10526316x + -8.585526316 + x2 = 0 + -8.585526316

Reorder the terms:
8.585526316 + -8.585526316 + -15.10526316x + x2 = 0 + -8.585526316

Combine like terms: 8.585526316 + -8.585526316 = 0.000000000
0.000000000 + -15.10526316x + x2 = 0 + -8.585526316
-15.10526316x + x2 = 0 + -8.585526316

Combine like terms: 0 + -8.585526316 = -8.585526316
-15.10526316x + x2 = -8.585526316

The x term is -15.10526316x.  Take half its coefficient (-7.55263158).
Square it (57.04224378) and add it to both sides.

Add '57.04224378' to each side of the equation.
-15.10526316x + 57.04224378 + x2 = -8.585526316 + 57.04224378

Reorder the terms:
57.04224378 + -15.10526316x + x2 = -8.585526316 + 57.04224378

Combine like terms: -8.585526316 + 57.04224378 = 48.456717464
57.04224378 + -15.10526316x + x2 = 48.456717464

Factor a perfect square on the left side:
(x + -7.55263158)(x + -7.55263158) = 48.456717464

Calculate the square root of the right side: 6.96108594

Break this problem into two subproblems by setting 
(x + -7.55263158) equal to 6.96108594 and -6.96108594.

Subproblem 1
x + -7.55263158 = 6.96108594

Simplifying
x + -7.55263158 = 6.96108594

Reorder the terms:
-7.55263158 + x = 6.96108594

Solving
-7.55263158 + x = 6.96108594

Solving for variable 'x'.

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

Add '7.55263158' to each side of the equation.
-7.55263158 + 7.55263158 + x = 6.96108594 + 7.55263158

Combine like terms: -7.55263158 + 7.55263158 = 0.00000000
0.00000000 + x = 6.96108594 + 7.55263158
x = 6.96108594 + 7.55263158

Combine like terms: 6.96108594 + 7.55263158 = 14.51371752
x = 14.51371752

Simplifying
x = 14.51371752

Subproblem 2
x + -7.55263158 = -6.96108594

Simplifying
x + -7.55263158 = -6.96108594

Reorder the terms:
-7.55263158 + x = -6.96108594

Solving
-7.55263158 + x = -6.96108594

Solving for variable 'x'.

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

Add '7.55263158' to each side of the equation.
-7.55263158 + 7.55263158 + x = -6.96108594 + 7.55263158

Combine like terms: -7.55263158 + 7.55263158 = 0.00000000
0.00000000 + x = -6.96108594 + 7.55263158
x = -6.96108594 + 7.55263158

Combine like terms: -6.96108594 + 7.55263158 = 0.59154564
x = 0.59154564

Simplifying
x = 0.59154564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.51371752, 0.59154564}