3x^2+8-12=16-9x

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Solution for 3x^2+8-12=16-9x equation: 


Simplifying
3x2 + 8 + -12 = 16 + -9x

Reorder the terms:
8 + -12 + 3x2 = 16 + -9x

Combine like terms: 8 + -12 = -4
-4 + 3x2 = 16 + -9x

Solving
-4 + 3x2 = 16 + -9x

Solving for variable 'x'.

Reorder the terms:
-4 + -16 + 9x + 3x2 = 16 + -9x + -16 + 9x

Combine like terms: -4 + -16 = -20
-20 + 9x + 3x2 = 16 + -9x + -16 + 9x

Reorder the terms:
-20 + 9x + 3x2 = 16 + -16 + -9x + 9x

Combine like terms: 16 + -16 = 0
-20 + 9x + 3x2 = 0 + -9x + 9x
-20 + 9x + 3x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-20 + 9x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + 3x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 3x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 3x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 3x + x2 = 0 + 6.666666667
3x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
3x + x2 = 6.666666667

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 = 6.666666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 6.666666667 + 2.25

Combine like terms: 6.666666667 + 2.25 = 8.916666667
2.25 + 3x + x2 = 8.916666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.986078811 and -2.986078811.


Subproblem 1
x + 1.5 = 2.986078811

Simplifying
x + 1.5 = 2.986078811

Reorder the terms:
1.5 + x = 2.986078811

Solving
1.5 + x = 2.986078811

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 = 2.986078811 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.986078811 + -1.5
x = 2.986078811 + -1.5

Combine like terms: 2.986078811 + -1.5 = 1.486078811
x = 1.486078811

Simplifying
x = 1.486078811


Subproblem 2
x + 1.5 = -2.986078811

Simplifying
x + 1.5 = -2.986078811

Reorder the terms:
1.5 + x = -2.986078811

Solving
1.5 + x = -2.986078811

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 = -2.986078811 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.986078811 + -1.5
x = -2.986078811 + -1.5

Combine like terms: -2.986078811 + -1.5 = -4.486078811
x = -4.486078811

Simplifying
x = -4.486078811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.486078811, -4.486078811}

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