12x^2-9x-9=0

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Solution for 12x^2-9x-9=0 equation: 


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

Reorder the terms:
-9 + -9x + 12x2 = 0

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

Solving for variable 'x'.

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

Ignore the factor 3.

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

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

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

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

Divide each side by '4'.
-0.75 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.75x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.75x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.75x + x2 = 0 + 0.75
-0.75x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.75x + x2 = 0.75

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.75 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.75 + 0.140625

Combine like terms: 0.75 + 0.140625 = 0.890625
0.140625 + -0.75x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + -0.375 = 0.943729304

Simplifying
x + -0.375 = 0.943729304

Reorder the terms:
-0.375 + x = 0.943729304

Solving
-0.375 + x = 0.943729304

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.943729304 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.943729304 + 0.375
x = 0.943729304 + 0.375

Combine like terms: 0.943729304 + 0.375 = 1.318729304
x = 1.318729304

Simplifying
x = 1.318729304


Subproblem 2
x + -0.375 = -0.943729304

Simplifying
x + -0.375 = -0.943729304

Reorder the terms:
-0.375 + x = -0.943729304

Solving
-0.375 + x = -0.943729304

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.943729304 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.943729304 + 0.375
x = -0.943729304 + 0.375

Combine like terms: -0.943729304 + 0.375 = -0.568729304
x = -0.568729304

Simplifying
x = -0.568729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.318729304, -0.568729304}
Solution
x = {1.318729304, -0.568729304}

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