3(x-2)*3(x-2)+4=52

Solution for 3(x-2)*3(x-2)+4=52 equation:

Simplifying
3(x + -2) * 3(x + -2) + 4 = 52

Reorder the terms:
3(-2 + x) * 3(x + -2) + 4 = 52

Reorder the terms:
3(-2 + x) * 3(-2 + x) + 4 = 52

Reorder the terms for easier multiplication:
3 * 3(-2 + x)(-2 + x) + 4 = 52

Multiply 3 * 3
9(-2 + x)(-2 + x) + 4 = 52

Multiply (-2 + x) * (-2 + x)
9(-2(-2 + x) + x(-2 + x)) + 4 = 52
9((-2 * -2 + x * -2) + x(-2 + x)) + 4 = 52
9((4 + -2x) + x(-2 + x)) + 4 = 52
9(4 + -2x + (-2 * x + x * x)) + 4 = 52
9(4 + -2x + (-2x + x2)) + 4 = 52

Combine like terms: -2x + -2x = -4x
9(4 + -4x + x2) + 4 = 52
(4 * 9 + -4x * 9 + x2 * 9) + 4 = 52
(36 + -36x + 9x2) + 4 = 52

Reorder the terms:
36 + 4 + -36x + 9x2 = 52

Combine like terms: 36 + 4 = 40
40 + -36x + 9x2 = 52

Solving
40 + -36x + 9x2 = 52

Solving for variable 'x'.

Reorder the terms:
40 + -52 + -36x + 9x2 = 52 + -52

Combine like terms: 40 + -52 = -12
-12 + -36x + 9x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-12 + -36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -12x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + -12x + 3x2 = 0

Solving
-4 + -12x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -4x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -4x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 1.333333333
-4x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-4x + x2 = 1.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.333333333 + 4

Reorder the terms:
4 + -4x + x2 = 1.333333333 + 4

Combine like terms: 1.333333333 + 4 = 5.333333333
4 + -4x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + -2) equal to 2.309401077 and -2.309401077.

Subproblem 1
x + -2 = 2.309401077

Simplifying
x + -2 = 2.309401077

Reorder the terms:
-2 + x = 2.309401077

Solving
-2 + x = 2.309401077

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.309401077 + 2
x = 2.309401077 + 2

Combine like terms: 2.309401077 + 2 = 4.309401077
x = 4.309401077

Simplifying
x = 4.309401077

Subproblem 2
x + -2 = -2.309401077

Simplifying
x + -2 = -2.309401077

Reorder the terms:
-2 + x = -2.309401077

Solving
-2 + x = -2.309401077

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.309401077 + 2
x = -2.309401077 + 2

Combine like terms: -2.309401077 + 2 = -0.309401077
x = -0.309401077

Simplifying
x = -0.309401077

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.309401077, -0.309401077}
Solution
x = {4.309401077, -0.309401077}