(3x-3)(3x-3)=21

Solution for (3x-3)(3x-3)=21 equation:

Simplifying
(3x + -3)(3x + -3) = 21

Reorder the terms:
(-3 + 3x)(3x + -3) = 21

Reorder the terms:
(-3 + 3x)(-3 + 3x) = 21

Multiply (-3 + 3x) * (-3 + 3x)
(-3(-3 + 3x) + 3x * (-3 + 3x)) = 21
((-3 * -3 + 3x * -3) + 3x * (-3 + 3x)) = 21
((9 + -9x) + 3x * (-3 + 3x)) = 21
(9 + -9x + (-3 * 3x + 3x * 3x)) = 21
(9 + -9x + (-9x + 9x2)) = 21

Combine like terms: -9x + -9x = -18x
(9 + -18x + 9x2) = 21

Solving
9 + -18x + 9x2 = 21

Solving for variable 'x'.

Reorder the terms:
9 + -21 + -18x + 9x2 = 21 + -21

Combine like terms: 9 + -21 = -12
-12 + -18x + 9x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-12 + -18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -6x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + -6x + 3x2 = 0

Solving
-4 + -6x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.333333333
-2x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2x + x2 = 1.333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.333333333 + 1

Reorder the terms:
1 + -2x + x2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + -2x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -1) equal to 1.527525232 and -1.527525232.

Subproblem 1
x + -1 = 1.527525232

Simplifying
x + -1 = 1.527525232

Reorder the terms:
-1 + x = 1.527525232

Solving
-1 + x = 1.527525232

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.527525232 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.527525232 + 1
x = 1.527525232 + 1

Combine like terms: 1.527525232 + 1 = 2.527525232
x = 2.527525232

Simplifying
x = 2.527525232

Subproblem 2
x + -1 = -1.527525232

Simplifying
x + -1 = -1.527525232

Reorder the terms:
-1 + x = -1.527525232

Solving
-1 + x = -1.527525232

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.527525232 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.527525232 + 1
x = -1.527525232 + 1

Combine like terms: -1.527525232 + 1 = -0.527525232
x = -0.527525232

Simplifying
x = -0.527525232

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.527525232, -0.527525232}
Solution
x = {2.527525232, -0.527525232}