12x^2-156x+380=0

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Solution for 12x^2-156x+380=0 equation: 


Simplifying
12x2 + -156x + 380 = 0

Reorder the terms:
380 + -156x + 12x2 = 0

Solving
380 + -156x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(95 + -39x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(95 + -39x + 3x2)' equal to zero and attempt to solve:

Simplifying
95 + -39x + 3x2 = 0

Solving
95 + -39x + 3x2 = 0

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

Divide each side by '3'.
31.66666667 + -13x + x2 = 0

Move the constant term to the right:

Add '-31.66666667' to each side of the equation.
31.66666667 + -13x + -31.66666667 + x2 = 0 + -31.66666667

Reorder the terms:
31.66666667 + -31.66666667 + -13x + x2 = 0 + -31.66666667

Combine like terms: 31.66666667 + -31.66666667 = 0.00000000
0.00000000 + -13x + x2 = 0 + -31.66666667
-13x + x2 = 0 + -31.66666667

Combine like terms: 0 + -31.66666667 = -31.66666667
-13x + x2 = -31.66666667

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -31.66666667 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -31.66666667 + 42.25

Combine like terms: -31.66666667 + 42.25 = 10.58333333
42.25 + -13x + x2 = 10.58333333

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 10.58333333

Calculate the square root of the right side: 3.253203549

Break this problem into two subproblems by setting 
(x + -6.5) equal to 3.253203549 and -3.253203549.


Subproblem 1
x + -6.5 = 3.253203549

Simplifying
x + -6.5 = 3.253203549

Reorder the terms:
-6.5 + x = 3.253203549

Solving
-6.5 + x = 3.253203549

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 3.253203549 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 3.253203549 + 6.5
x = 3.253203549 + 6.5

Combine like terms: 3.253203549 + 6.5 = 9.753203549
x = 9.753203549

Simplifying
x = 9.753203549


Subproblem 2
x + -6.5 = -3.253203549

Simplifying
x + -6.5 = -3.253203549

Reorder the terms:
-6.5 + x = -3.253203549

Solving
-6.5 + x = -3.253203549

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -3.253203549 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -3.253203549 + 6.5
x = -3.253203549 + 6.5

Combine like terms: -3.253203549 + 6.5 = 3.246796451
x = 3.246796451

Simplifying
x = 3.246796451


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.753203549, 3.246796451}
Solution
x = {9.753203549, 3.246796451}

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