12x^2-360x+200=0

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Solution for 12x^2-360x+200=0 equation: 


Simplifying
12x2 + -360x + 200 = 0

Reorder the terms:
200 + -360x + 12x2 = 0

Solving
200 + -360x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + -90x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50 + -90x + 3x2)' equal to zero and attempt to solve:

Simplifying
50 + -90x + 3x2 = 0

Solving
50 + -90x + 3x2 = 0

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

Divide each side by '3'.
16.66666667 + -30x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + -30x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + -30x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + -30x + x2 = 0 + -16.66666667
-30x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
-30x + x2 = -16.66666667

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -16.66666667 + 225

Reorder the terms:
225 + -30x + x2 = -16.66666667 + 225

Combine like terms: -16.66666667 + 225 = 208.33333333
225 + -30x + x2 = 208.33333333

Factor a perfect square on the left side:
(x + -15)(x + -15) = 208.33333333

Calculate the square root of the right side: 14.43375673

Break this problem into two subproblems by setting 
(x + -15) equal to 14.43375673 and -14.43375673.


Subproblem 1
x + -15 = 14.43375673

Simplifying
x + -15 = 14.43375673

Reorder the terms:
-15 + x = 14.43375673

Solving
-15 + x = 14.43375673

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 14.43375673 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.43375673 + 15
x = 14.43375673 + 15

Combine like terms: 14.43375673 + 15 = 29.43375673
x = 29.43375673

Simplifying
x = 29.43375673


Subproblem 2
x + -15 = -14.43375673

Simplifying
x + -15 = -14.43375673

Reorder the terms:
-15 + x = -14.43375673

Solving
-15 + x = -14.43375673

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -14.43375673 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.43375673 + 15
x = -14.43375673 + 15

Combine like terms: -14.43375673 + 15 = 0.56624327
x = 0.56624327

Simplifying
x = 0.56624327


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.43375673, 0.56624327}
Solution
x = {29.43375673, 0.56624327}

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