12x^2-76x+20=0

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Solution for 12x^2-76x+20=0 equation: 


Simplifying
12x2 + -76x + 20 = 0

Reorder the terms:
20 + -76x + 12x2 = 0

Solving
20 + -76x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -19x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -19x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + -19x + 3x2 = 0

Solving
5 + -19x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -6.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -6.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -6.333333333x + x2 = 0 + -1.666666667
-6.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-6.333333333x + x2 = -1.666666667

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = -1.666666667 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = -1.666666667 + 10.02777778

Combine like terms: -1.666666667 + 10.02777778 = 8.361111113
10.02777778 + -6.333333333x + x2 = 8.361111113

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 8.361111113

Calculate the square root of the right side: 2.891558596

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 2.891558596 and -2.891558596.


Subproblem 1
x + -3.166666667 = 2.891558596

Simplifying
x + -3.166666667 = 2.891558596

Reorder the terms:
-3.166666667 + x = 2.891558596

Solving
-3.166666667 + x = 2.891558596

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 2.891558596 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 2.891558596 + 3.166666667
x = 2.891558596 + 3.166666667

Combine like terms: 2.891558596 + 3.166666667 = 6.058225263
x = 6.058225263

Simplifying
x = 6.058225263


Subproblem 2
x + -3.166666667 = -2.891558596

Simplifying
x + -3.166666667 = -2.891558596

Reorder the terms:
-3.166666667 + x = -2.891558596

Solving
-3.166666667 + x = -2.891558596

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -2.891558596 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -2.891558596 + 3.166666667
x = -2.891558596 + 3.166666667

Combine like terms: -2.891558596 + 3.166666667 = 0.275108071
x = 0.275108071

Simplifying
x = 0.275108071


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.058225263, 0.275108071}
Solution
x = {6.058225263, 0.275108071}

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