3(x-3)6x=24+8x

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Solution for 3(x-3)6x=24+8x equation: 


Simplifying
3(x + -3) * 6x = 24 + 8x

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

Reorder the terms for easier multiplication:
3 * 6x(-3 + x) = 24 + 8x

Multiply 3 * 6
18x(-3 + x) = 24 + 8x
(-3 * 18x + x * 18x) = 24 + 8x
(-54x + 18x2) = 24 + 8x

Solving
-54x + 18x2 = 24 + 8x

Solving for variable 'x'.

Reorder the terms:
-24 + -54x + -8x + 18x2 = 24 + 8x + -24 + -8x

Combine like terms: -54x + -8x = -62x
-24 + -62x + 18x2 = 24 + 8x + -24 + -8x

Reorder the terms:
-24 + -62x + 18x2 = 24 + -24 + 8x + -8x

Combine like terms: 24 + -24 = 0
-24 + -62x + 18x2 = 0 + 8x + -8x
-24 + -62x + 18x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-24 + -62x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -31x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + -31x + 9x2)' equal to zero and attempt to solve:

Simplifying
-12 + -31x + 9x2 = 0

Solving
-12 + -31x + 9x2 = 0

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

Divide each side by '9'.
-1.333333333 + -3.444444444x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3.444444444x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3.444444444x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3.444444444x + x2 = 0 + 1.333333333
-3.444444444x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3.444444444x + x2 = 1.333333333

The x term is -3.444444444x.  Take half its coefficient (-1.722222222).
Square it (2.966049382) and add it to both sides.

Add '2.966049382' to each side of the equation.
-3.444444444x + 2.966049382 + x2 = 1.333333333 + 2.966049382

Reorder the terms:
2.966049382 + -3.444444444x + x2 = 1.333333333 + 2.966049382

Combine like terms: 1.333333333 + 2.966049382 = 4.299382715
2.966049382 + -3.444444444x + x2 = 4.299382715

Factor a perfect square on the left side:
(x + -1.722222222)(x + -1.722222222) = 4.299382715

Calculate the square root of the right side: 2.073495289

Break this problem into two subproblems by setting 
(x + -1.722222222) equal to 2.073495289 and -2.073495289.


Subproblem 1
x + -1.722222222 = 2.073495289

Simplifying
x + -1.722222222 = 2.073495289

Reorder the terms:
-1.722222222 + x = 2.073495289

Solving
-1.722222222 + x = 2.073495289

Solving for variable 'x'.

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

Add '1.722222222' to each side of the equation.
-1.722222222 + 1.722222222 + x = 2.073495289 + 1.722222222

Combine like terms: -1.722222222 + 1.722222222 = 0.000000000
0.000000000 + x = 2.073495289 + 1.722222222
x = 2.073495289 + 1.722222222

Combine like terms: 2.073495289 + 1.722222222 = 3.795717511
x = 3.795717511

Simplifying
x = 3.795717511


Subproblem 2
x + -1.722222222 = -2.073495289

Simplifying
x + -1.722222222 = -2.073495289

Reorder the terms:
-1.722222222 + x = -2.073495289

Solving
-1.722222222 + x = -2.073495289

Solving for variable 'x'.

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

Add '1.722222222' to each side of the equation.
-1.722222222 + 1.722222222 + x = -2.073495289 + 1.722222222

Combine like terms: -1.722222222 + 1.722222222 = 0.000000000
0.000000000 + x = -2.073495289 + 1.722222222
x = -2.073495289 + 1.722222222

Combine like terms: -2.073495289 + 1.722222222 = -0.351273067
x = -0.351273067

Simplifying
x = -0.351273067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.795717511, -0.351273067}
Solution
x = {3.795717511, -0.351273067}

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