8-12x=6x(1+x)

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Solution for 8-12x=6x(1+x) equation:


Simplifying
8 + -12x = 6x(1 + x)
8 + -12x = (1 * 6x + x * 6x)
8 + -12x = (6x + 6x2)

Solving
8 + -12x = 6x + 6x2

Solving for variable 'x'.

Combine like terms: -12x + -6x = -18x
8 + -18x + -6x2 = 6x + 6x2 + -6x + -6x2

Reorder the terms:
8 + -18x + -6x2 = 6x + -6x + 6x2 + -6x2

Combine like terms: 6x + -6x = 0
8 + -18x + -6x2 = 0 + 6x2 + -6x2
8 + -18x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
8 + -18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -9x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -9x + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + -9x + -3x2 = 0

Solving
4 + -9x + -3x2 = 0

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

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

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 3x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 3x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + 1.333333333
3x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
3x + x2 = 1.333333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1.333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.333333333 + 2.25

Combine like terms: 1.333333333 + 2.25 = 3.583333333
2.25 + 3x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
x + 1.5 = 1.892969449

Simplifying
x + 1.5 = 1.892969449

Reorder the terms:
1.5 + x = 1.892969449

Solving
1.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.892969449 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.892969449 + -1.5
x = 1.892969449 + -1.5

Combine like terms: 1.892969449 + -1.5 = 0.392969449
x = 0.392969449

Simplifying
x = 0.392969449


Subproblem 2
x + 1.5 = -1.892969449

Simplifying
x + 1.5 = -1.892969449

Reorder the terms:
1.5 + x = -1.892969449

Solving
1.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.892969449 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.892969449 + -1.5
x = -1.892969449 + -1.5

Combine like terms: -1.892969449 + -1.5 = -3.392969449
x = -3.392969449

Simplifying
x = -3.392969449


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.392969449, -3.392969449}
Solution
x = {0.392969449, -3.392969449}

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