6x(x-2)=8

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


Simplifying
6x(x + -2) = 8

Reorder the terms:
6x(-2 + x) = 8
(-2 * 6x + x * 6x) = 8
(-12x + 6x2) = 8

Solving
-12x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -12x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -6x + 3x2) = 0

Ignore the factor 2.

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}

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