3x(2x-2)-4(x+6)=3x+8+x

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Solution for 3x(2x-2)-4(x+6)=3x+8+x equation: 


Simplifying
3x(2x + -2) + -4(x + 6) = 3x + 8 + x

Reorder the terms:
3x(-2 + 2x) + -4(x + 6) = 3x + 8 + x
(-2 * 3x + 2x * 3x) + -4(x + 6) = 3x + 8 + x
(-6x + 6x2) + -4(x + 6) = 3x + 8 + x

Reorder the terms:
-6x + 6x2 + -4(6 + x) = 3x + 8 + x
-6x + 6x2 + (6 * -4 + x * -4) = 3x + 8 + x
-6x + 6x2 + (-24 + -4x) = 3x + 8 + x

Reorder the terms:
-24 + -6x + -4x + 6x2 = 3x + 8 + x

Combine like terms: -6x + -4x = -10x
-24 + -10x + 6x2 = 3x + 8 + x

Reorder the terms:
-24 + -10x + 6x2 = 8 + 3x + x

Combine like terms: 3x + x = 4x
-24 + -10x + 6x2 = 8 + 4x

Solving
-24 + -10x + 6x2 = 8 + 4x

Solving for variable 'x'.

Reorder the terms:
-24 + -8 + -10x + -4x + 6x2 = 8 + 4x + -8 + -4x

Combine like terms: -24 + -8 = -32
-32 + -10x + -4x + 6x2 = 8 + 4x + -8 + -4x

Combine like terms: -10x + -4x = -14x
-32 + -14x + 6x2 = 8 + 4x + -8 + -4x

Reorder the terms:
-32 + -14x + 6x2 = 8 + -8 + 4x + -4x

Combine like terms: 8 + -8 = 0
-32 + -14x + 6x2 = 0 + 4x + -4x
-32 + -14x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-32 + -14x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -7x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -7x + 3x2)' equal to zero and attempt to solve:

Simplifying
-16 + -7x + 3x2 = 0

Solving
-16 + -7x + 3x2 = 0

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

Divide each side by '3'.
-5.333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -2.333333333x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -2.333333333x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 5.333333333
-2.333333333x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-2.333333333x + x2 = 5.333333333

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 5.333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 5.333333333 + 1.361111112

Combine like terms: 5.333333333 + 1.361111112 = 6.694444445
1.361111112 + -2.333333333x + x2 = 6.694444445

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 6.694444445

Calculate the square root of the right side: 2.587362449

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.587362449 and -2.587362449.


Subproblem 1
x + -1.166666667 = 2.587362449

Simplifying
x + -1.166666667 = 2.587362449

Reorder the terms:
-1.166666667 + x = 2.587362449

Solving
-1.166666667 + x = 2.587362449

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 2.587362449 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 2.587362449 + 1.166666667
x = 2.587362449 + 1.166666667

Combine like terms: 2.587362449 + 1.166666667 = 3.754029116
x = 3.754029116

Simplifying
x = 3.754029116


Subproblem 2
x + -1.166666667 = -2.587362449

Simplifying
x + -1.166666667 = -2.587362449

Reorder the terms:
-1.166666667 + x = -2.587362449

Solving
-1.166666667 + x = -2.587362449

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -2.587362449 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -2.587362449 + 1.166666667
x = -2.587362449 + 1.166666667

Combine like terms: -2.587362449 + 1.166666667 = -1.420695782
x = -1.420695782

Simplifying
x = -1.420695782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.754029116, -1.420695782}
Solution
x = {3.754029116, -1.420695782}

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