3[(x-2)(x-2)]+4(x-2)=252

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Solution for 3[(x-2)(x-2)]+4(x-2)=252 equation: 


Simplifying
3[(x + -2)(x + -2)] + 4(x + -2) = 252

Reorder the terms:
3[(-2 + x)(x + -2)] + 4(x + -2) = 252

Reorder the terms:
3[(-2 + x)(-2 + x)] + 4(x + -2) = 252

Multiply (-2 + x) * (-2 + x)
3[(-2(-2 + x) + x(-2 + x))] + 4(x + -2) = 252
3[((-2 * -2 + x * -2) + x(-2 + x))] + 4(x + -2) = 252
3[((4 + -2x) + x(-2 + x))] + 4(x + -2) = 252
3[(4 + -2x + (-2 * x + x * x))] + 4(x + -2) = 252
3[(4 + -2x + (-2x + x2))] + 4(x + -2) = 252

Combine like terms: -2x + -2x = -4x
3[(4 + -4x + x2)] + 4(x + -2) = 252
[4 * 3 + -4x * 3 + x2 * 3] + 4(x + -2) = 252
[12 + -12x + 3x2] + 4(x + -2) = 252

Reorder the terms:
12 + -12x + 3x2 + 4(-2 + x) = 252
12 + -12x + 3x2 + (-2 * 4 + x * 4) = 252
12 + -12x + 3x2 + (-8 + 4x) = 252

Reorder the terms:
12 + -8 + -12x + 4x + 3x2 = 252

Combine like terms: 12 + -8 = 4
4 + -12x + 4x + 3x2 = 252

Combine like terms: -12x + 4x = -8x
4 + -8x + 3x2 = 252

Solving
4 + -8x + 3x2 = 252

Solving for variable 'x'.

Reorder the terms:
4 + -252 + -8x + 3x2 = 252 + -252

Combine like terms: 4 + -252 = -248
-248 + -8x + 3x2 = 252 + -252

Combine like terms: 252 + -252 = 0
-248 + -8x + 3x2 = 0

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

Divide each side by '3'.
-82.66666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '82.66666667' to each side of the equation.
-82.66666667 + -2.666666667x + 82.66666667 + x2 = 0 + 82.66666667

Reorder the terms:
-82.66666667 + 82.66666667 + -2.666666667x + x2 = 0 + 82.66666667

Combine like terms: -82.66666667 + 82.66666667 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 82.66666667
-2.666666667x + x2 = 0 + 82.66666667

Combine like terms: 0 + 82.66666667 = 82.66666667
-2.666666667x + x2 = 82.66666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 82.66666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 82.66666667 + 1.777777780

Combine like terms: 82.66666667 + 1.777777780 = 84.44444445
1.777777780 + -2.666666667x + x2 = 84.44444445

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 84.44444445

Calculate the square root of the right side: 9.189365835

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 9.189365835 and -9.189365835.


Subproblem 1
x + -1.333333334 = 9.189365835

Simplifying
x + -1.333333334 = 9.189365835

Reorder the terms:
-1.333333334 + x = 9.189365835

Solving
-1.333333334 + x = 9.189365835

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 9.189365835 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 9.189365835 + 1.333333334
x = 9.189365835 + 1.333333334

Combine like terms: 9.189365835 + 1.333333334 = 10.522699169
x = 10.522699169

Simplifying
x = 10.522699169


Subproblem 2
x + -1.333333334 = -9.189365835

Simplifying
x + -1.333333334 = -9.189365835

Reorder the terms:
-1.333333334 + x = -9.189365835

Solving
-1.333333334 + x = -9.189365835

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -9.189365835 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -9.189365835 + 1.333333334
x = -9.189365835 + 1.333333334

Combine like terms: -9.189365835 + 1.333333334 = -7.856032501
x = -7.856032501

Simplifying
x = -7.856032501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.522699169, -7.856032501}

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