-9x^2+12x+3=0

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Solution for -9x^2+12x+3=0 equation: 


Simplifying
-9x2 + 12x + 3 = 0

Reorder the terms:
3 + 12x + -9x2 = 0

Solving
3 + 12x + -9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4x + -3x2) = 0

Ignore the factor 3.

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

Simplifying
1 + 4x + -3x2 = 0

Solving
1 + 4x + -3x2 = 0

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

Divide each side by '-3'.
-0.3333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -1.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -1.333333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.3333333333
-1.333333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-1.333333333x + x2 = 0.3333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 0.3333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.3333333333 + 0.4444444442

Combine like terms: 0.3333333333 + 0.4444444442 = 0.7777777775
0.4444444442 + -1.333333333x + x2 = 0.7777777775

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.7777777775

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.881917104 and -0.881917104.


Subproblem 1
x + -0.6666666665 = 0.881917104

Simplifying
x + -0.6666666665 = 0.881917104

Reorder the terms:
-0.6666666665 + x = 0.881917104

Solving
-0.6666666665 + x = 0.881917104

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 0.881917104 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 0.881917104 + 0.6666666665
x = 0.881917104 + 0.6666666665

Combine like terms: 0.881917104 + 0.6666666665 = 1.5485837705
x = 1.5485837705

Simplifying
x = 1.5485837705


Subproblem 2
x + -0.6666666665 = -0.881917104

Simplifying
x + -0.6666666665 = -0.881917104

Reorder the terms:
-0.6666666665 + x = -0.881917104

Solving
-0.6666666665 + x = -0.881917104

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -0.881917104 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -0.881917104 + 0.6666666665
x = -0.881917104 + 0.6666666665

Combine like terms: -0.881917104 + 0.6666666665 = -0.2152504375
x = -0.2152504375

Simplifying
x = -0.2152504375


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5485837705, -0.2152504375}
Solution
x = {1.5485837705, -0.2152504375}

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