3[3-3(x+1)]+1=2(-20-x)2x+20

Solution for 3[3-3(x+1)]+1=2(-20-x)2x+20 equation:

Simplifying
3[3 + -3(x + 1)] + 1 = 2(-20 + -1x) * 2x + 20

Reorder the terms:
3[3 + -3(1 + x)] + 1 = 2(-20 + -1x) * 2x + 20
3[3 + (1 * -3 + x * -3)] + 1 = 2(-20 + -1x) * 2x + 20
3[3 + (-3 + -3x)] + 1 = 2(-20 + -1x) * 2x + 20

Combine like terms: 3 + -3 = 0
3[0 + -3x] + 1 = 2(-20 + -1x) * 2x + 20
3[-3x] + 1 = 2(-20 + -1x) * 2x + 20

Remove brackets around [-3x]
3 * -3x + 1 = 2(-20 + -1x) * 2x + 20

Multiply 3 * -3
-9x + 1 = 2(-20 + -1x) * 2x + 20

Reorder the terms:
1 + -9x = 2(-20 + -1x) * 2x + 20

Reorder the terms for easier multiplication:
1 + -9x = 2 * 2x(-20 + -1x) + 20

Multiply 2 * 2
1 + -9x = 4x(-20 + -1x) + 20
1 + -9x = (-20 * 4x + -1x * 4x) + 20
1 + -9x = (-80x + -4x2) + 20

Reorder the terms:
1 + -9x = 20 + -80x + -4x2

Solving
1 + -9x = 20 + -80x + -4x2

Solving for variable 'x'.

Reorder the terms:
1 + -20 + -9x + 80x + 4x2 = 20 + -80x + -4x2 + -20 + 80x + 4x2

Combine like terms: 1 + -20 = -19
-19 + -9x + 80x + 4x2 = 20 + -80x + -4x2 + -20 + 80x + 4x2

Combine like terms: -9x + 80x = 71x
-19 + 71x + 4x2 = 20 + -80x + -4x2 + -20 + 80x + 4x2

Reorder the terms:
-19 + 71x + 4x2 = 20 + -20 + -80x + 80x + -4x2 + 4x2

Combine like terms: 20 + -20 = 0
-19 + 71x + 4x2 = 0 + -80x + 80x + -4x2 + 4x2
-19 + 71x + 4x2 = -80x + 80x + -4x2 + 4x2

Combine like terms: -80x + 80x = 0
-19 + 71x + 4x2 = 0 + -4x2 + 4x2
-19 + 71x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-19 + 71x + 4x2 = 0

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

Divide each side by '4'.
-4.75 + 17.75x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 17.75x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 17.75x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 17.75x + x2 = 0 + 4.75
17.75x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
17.75x + x2 = 4.75

The x term is 17.75x.  Take half its coefficient (8.875).
Square it (78.765625) and add it to both sides.

Add '78.765625' to each side of the equation.
17.75x + 78.765625 + x2 = 4.75 + 78.765625

Reorder the terms:
78.765625 + 17.75x + x2 = 4.75 + 78.765625

Combine like terms: 4.75 + 78.765625 = 83.515625
78.765625 + 17.75x + x2 = 83.515625

Factor a perfect square on the left side:
(x + 8.875)(x + 8.875) = 83.515625

Calculate the square root of the right side: 9.138688363

Break this problem into two subproblems by setting 
(x + 8.875) equal to 9.138688363 and -9.138688363.

Subproblem 1
x + 8.875 = 9.138688363

Simplifying
x + 8.875 = 9.138688363

Reorder the terms:
8.875 + x = 9.138688363

Solving
8.875 + x = 9.138688363

Solving for variable 'x'.

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

Add '-8.875' to each side of the equation.
8.875 + -8.875 + x = 9.138688363 + -8.875

Combine like terms: 8.875 + -8.875 = 0.000
0.000 + x = 9.138688363 + -8.875
x = 9.138688363 + -8.875

Combine like terms: 9.138688363 + -8.875 = 0.263688363
x = 0.263688363

Simplifying
x = 0.263688363

Subproblem 2
x + 8.875 = -9.138688363

Simplifying
x + 8.875 = -9.138688363

Reorder the terms:
8.875 + x = -9.138688363

Solving
8.875 + x = -9.138688363

Solving for variable 'x'.

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

Add '-8.875' to each side of the equation.
8.875 + -8.875 + x = -9.138688363 + -8.875

Combine like terms: 8.875 + -8.875 = 0.000
0.000 + x = -9.138688363 + -8.875
x = -9.138688363 + -8.875

Combine like terms: -9.138688363 + -8.875 = -18.013688363
x = -18.013688363

Simplifying
x = -18.013688363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.263688363, -18.013688363}