12x^2-18x+4=0

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Solution for 12x^2-18x+4=0 equation: 


Simplifying
12x2 + -18x + 4 = 0

Reorder the terms:
4 + -18x + 12x2 = 0

Solving
4 + -18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -9x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -9x + 6x2)' equal to zero and attempt to solve:

Simplifying
2 + -9x + 6x2 = 0

Solving
2 + -9x + 6x2 = 0

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

Divide each side by '6'.
0.3333333333 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.5x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.5x + x2 = 0 + -0.3333333333
-1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.5x + x2 = -0.3333333333

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.3333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.3333333333 + 0.5625

Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667
0.5625 + -1.5x + x2 = 0.2291666667

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.478713554 and -0.478713554.


Subproblem 1
x + -0.75 = 0.478713554

Simplifying
x + -0.75 = 0.478713554

Reorder the terms:
-0.75 + x = 0.478713554

Solving
-0.75 + x = 0.478713554

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.478713554 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.478713554 + 0.75
x = 0.478713554 + 0.75

Combine like terms: 0.478713554 + 0.75 = 1.228713554
x = 1.228713554

Simplifying
x = 1.228713554


Subproblem 2
x + -0.75 = -0.478713554

Simplifying
x + -0.75 = -0.478713554

Reorder the terms:
-0.75 + x = -0.478713554

Solving
-0.75 + x = -0.478713554

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.478713554 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.478713554 + 0.75
x = -0.478713554 + 0.75

Combine like terms: -0.478713554 + 0.75 = 0.271286446
x = 0.271286446

Simplifying
x = 0.271286446


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.228713554, 0.271286446}
Solution
x = {1.228713554, 0.271286446}

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