-3x(x-4)=8-3x

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


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

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

Solving
12x + -3x2 = 8 + -3x

Solving for variable 'x'.

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

Combine like terms: 12x + 3x = 15x
-8 + 15x + -3x2 = 8 + -3x + -8 + 3x

Reorder the terms:
-8 + 15x + -3x2 = 8 + -8 + -3x + 3x

Combine like terms: 8 + -8 = 0
-8 + 15x + -3x2 = 0 + -3x + 3x
-8 + 15x + -3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-8 + 15x + -3x2 = 0

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

Divide each side by '-3'.
2.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -5x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -5x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + -2.666666667
-5x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-5x + x2 = -2.666666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.666666667 + 6.25

Combine like terms: -2.666666667 + 6.25 = 3.583333333
6.25 + -5x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
x + -2.5 = 1.892969449

Simplifying
x + -2.5 = 1.892969449

Reorder the terms:
-2.5 + x = 1.892969449

Solving
-2.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.892969449 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.892969449 + 2.5
x = 1.892969449 + 2.5

Combine like terms: 1.892969449 + 2.5 = 4.392969449
x = 4.392969449

Simplifying
x = 4.392969449


Subproblem 2
x + -2.5 = -1.892969449

Simplifying
x + -2.5 = -1.892969449

Reorder the terms:
-2.5 + x = -1.892969449

Solving
-2.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.892969449 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.892969449 + 2.5
x = -1.892969449 + 2.5

Combine like terms: -1.892969449 + 2.5 = 0.607030551
x = 0.607030551

Simplifying
x = 0.607030551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.392969449, 0.607030551}

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