3(3x^2-10x-6)=0

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Solution for 3(3x^2-10x-6)=0 equation: 


Simplifying
3(3x2 + -10x + -6) = 0

Reorder the terms:
3(-6 + -10x + 3x2) = 0
(-6 * 3 + -10x * 3 + 3x2 * 3) = 0
(-18 + -30x + 9x2) = 0

Solving
-18 + -30x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -10x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-6 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
-6 + -10x + 3x2 = 0

Solving
-6 + -10x + 3x2 = 0

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

Divide each side by '3'.
-2 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.333333333x + x2 = 0 + 2
-3.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.333333333x + x2 = 2

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 2 + 2.777777779

Combine like terms: 2 + 2.777777779 = 4.777777779
2.777777779 + -3.333333333x + x2 = 4.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 4.777777779

Calculate the square root of the right side: 2.185812842

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.185812842 and -2.185812842.


Subproblem 1
x + -1.666666667 = 2.185812842

Simplifying
x + -1.666666667 = 2.185812842

Reorder the terms:
-1.666666667 + x = 2.185812842

Solving
-1.666666667 + x = 2.185812842

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.185812842 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.185812842 + 1.666666667
x = 2.185812842 + 1.666666667

Combine like terms: 2.185812842 + 1.666666667 = 3.852479509
x = 3.852479509

Simplifying
x = 3.852479509


Subproblem 2
x + -1.666666667 = -2.185812842

Simplifying
x + -1.666666667 = -2.185812842

Reorder the terms:
-1.666666667 + x = -2.185812842

Solving
-1.666666667 + x = -2.185812842

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.185812842 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.185812842 + 1.666666667
x = -2.185812842 + 1.666666667

Combine like terms: -2.185812842 + 1.666666667 = -0.519146175
x = -0.519146175

Simplifying
x = -0.519146175


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.852479509, -0.519146175}
Solution
x = {3.852479509, -0.519146175}

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