(3x+1)2=8x-(2-3x)(2+3x)

Solution for (3x+1)2=8x-(2-3x)(2+3x) equation:

Simplifying
(3x + 1) * 2 = 8x + -1(2 + -3x)(2 + 3x)

Reorder the terms:
(1 + 3x) * 2 = 8x + -1(2 + -3x)(2 + 3x)

Reorder the terms for easier multiplication:
2(1 + 3x) = 8x + -1(2 + -3x)(2 + 3x)
(1 * 2 + 3x * 2) = 8x + -1(2 + -3x)(2 + 3x)
(2 + 6x) = 8x + -1(2 + -3x)(2 + 3x)

Multiply (2 + -3x) * (2 + 3x)
2 + 6x = 8x + -1(2(2 + 3x) + -3x * (2 + 3x))
2 + 6x = 8x + -1((2 * 2 + 3x * 2) + -3x * (2 + 3x))
2 + 6x = 8x + -1((4 + 6x) + -3x * (2 + 3x))
2 + 6x = 8x + -1(4 + 6x + (2 * -3x + 3x * -3x))
2 + 6x = 8x + -1(4 + 6x + (-6x + -9x2))

Combine like terms: 6x + -6x = 0
2 + 6x = 8x + -1(4 + 0 + -9x2)
2 + 6x = 8x + -1(4 + -9x2)
2 + 6x = 8x + (4 * -1 + -9x2 * -1)
2 + 6x = 8x + (-4 + 9x2)

Reorder the terms:
2 + 6x = -4 + 8x + 9x2

Solving
2 + 6x = -4 + 8x + 9x2

Solving for variable 'x'.

Reorder the terms:
2 + 4 + 6x + -8x + -9x2 = -4 + 8x + 9x2 + 4 + -8x + -9x2

Combine like terms: 2 + 4 = 6
6 + 6x + -8x + -9x2 = -4 + 8x + 9x2 + 4 + -8x + -9x2

Combine like terms: 6x + -8x = -2x
6 + -2x + -9x2 = -4 + 8x + 9x2 + 4 + -8x + -9x2

Reorder the terms:
6 + -2x + -9x2 = -4 + 4 + 8x + -8x + 9x2 + -9x2

Combine like terms: -4 + 4 = 0
6 + -2x + -9x2 = 0 + 8x + -8x + 9x2 + -9x2
6 + -2x + -9x2 = 8x + -8x + 9x2 + -9x2

Combine like terms: 8x + -8x = 0
6 + -2x + -9x2 = 0 + 9x2 + -9x2
6 + -2x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
6 + -2x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.6666666667 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.2222222222x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.2222222222x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.2222222222x + x2 = 0 + 0.6666666667
0.2222222222x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.2222222222x + x2 = 0.6666666667

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 0.6666666667 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 0.6666666667 + 0.01234567901

Combine like terms: 0.6666666667 + 0.01234567901 = 0.67901234571
0.01234567901 + 0.2222222222x + x2 = 0.67901234571

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 0.67901234571

Calculate the square root of the right side: 0.824022054

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 0.824022054 and -0.824022054.

Subproblem 1
x + 0.1111111111 = 0.824022054

Simplifying
x + 0.1111111111 = 0.824022054

Reorder the terms:
0.1111111111 + x = 0.824022054

Solving
0.1111111111 + x = 0.824022054

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = 0.824022054 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = 0.824022054 + -0.1111111111
x = 0.824022054 + -0.1111111111

Combine like terms: 0.824022054 + -0.1111111111 = 0.7129109429
x = 0.7129109429

Simplifying
x = 0.7129109429

Subproblem 2
x + 0.1111111111 = -0.824022054

Simplifying
x + 0.1111111111 = -0.824022054

Reorder the terms:
0.1111111111 + x = -0.824022054

Solving
0.1111111111 + x = -0.824022054

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = -0.824022054 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = -0.824022054 + -0.1111111111
x = -0.824022054 + -0.1111111111

Combine like terms: -0.824022054 + -0.1111111111 = -0.9351331651
x = -0.9351331651

Simplifying
x = -0.9351331651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7129109429, -0.9351331651}