(4x-2)*3x=122

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Solution for (4x-2)*3x=122 equation: 


Simplifying
(4x + -2) * 3x = 122

Reorder the terms:
(-2 + 4x) * 3x = 122

Reorder the terms for easier multiplication:
3x(-2 + 4x) = 122
(-2 * 3x + 4x * 3x) = 122
(-6x + 12x2) = 122

Solving
-6x + 12x2 = 122

Solving for variable 'x'.

Reorder the terms:
-122 + -6x + 12x2 = 122 + -122

Combine like terms: 122 + -122 = 0
-122 + -6x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + -3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-61 + -3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-61 + -3x + 6x2 = 0

Solving
-61 + -3x + 6x2 = 0

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

Divide each side by '6'.
-10.16666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '10.16666667' to each side of the equation.
-10.16666667 + -0.5x + 10.16666667 + x2 = 0 + 10.16666667

Reorder the terms:
-10.16666667 + 10.16666667 + -0.5x + x2 = 0 + 10.16666667

Combine like terms: -10.16666667 + 10.16666667 = 0.00000000
0.00000000 + -0.5x + x2 = 0 + 10.16666667
-0.5x + x2 = 0 + 10.16666667

Combine like terms: 0 + 10.16666667 = 10.16666667
-0.5x + x2 = 10.16666667

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 10.16666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 10.16666667 + 0.0625

Combine like terms: 10.16666667 + 0.0625 = 10.22916667
0.0625 + -0.5x + x2 = 10.22916667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 10.22916667

Calculate the square root of the right side: 3.198306844

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.198306844 and -3.198306844.


Subproblem 1
x + -0.25 = 3.198306844

Simplifying
x + -0.25 = 3.198306844

Reorder the terms:
-0.25 + x = 3.198306844

Solving
-0.25 + x = 3.198306844

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 3.198306844 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 3.198306844 + 0.25
x = 3.198306844 + 0.25

Combine like terms: 3.198306844 + 0.25 = 3.448306844
x = 3.448306844

Simplifying
x = 3.448306844


Subproblem 2
x + -0.25 = -3.198306844

Simplifying
x + -0.25 = -3.198306844

Reorder the terms:
-0.25 + x = -3.198306844

Solving
-0.25 + x = -3.198306844

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -3.198306844 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -3.198306844 + 0.25
x = -3.198306844 + 0.25

Combine like terms: -3.198306844 + 0.25 = -2.948306844
x = -2.948306844

Simplifying
x = -2.948306844


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.448306844, -2.948306844}
Solution
x = {3.448306844, -2.948306844}

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