3x^2-5x=6x^2-6x-12x+2

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Solution for 3x^2-5x=6x^2-6x-12x+2 equation:


Simplifying
3x2 + -5x = 6x2 + -6x + -12x + 2

Reorder the terms:
-5x + 3x2 = 6x2 + -6x + -12x + 2

Reorder the terms:
-5x + 3x2 = 2 + -6x + -12x + 6x2

Combine like terms: -6x + -12x = -18x
-5x + 3x2 = 2 + -18x + 6x2

Solving
-5x + 3x2 = 2 + -18x + 6x2

Solving for variable 'x'.

Reorder the terms:
-2 + -5x + 18x + 3x2 + -6x2 = 2 + -18x + 6x2 + -2 + 18x + -6x2

Combine like terms: -5x + 18x = 13x
-2 + 13x + 3x2 + -6x2 = 2 + -18x + 6x2 + -2 + 18x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
-2 + 13x + -3x2 = 2 + -18x + 6x2 + -2 + 18x + -6x2

Reorder the terms:
-2 + 13x + -3x2 = 2 + -2 + -18x + 18x + 6x2 + -6x2

Combine like terms: 2 + -2 = 0
-2 + 13x + -3x2 = 0 + -18x + 18x + 6x2 + -6x2
-2 + 13x + -3x2 = -18x + 18x + 6x2 + -6x2

Combine like terms: -18x + 18x = 0
-2 + 13x + -3x2 = 0 + 6x2 + -6x2
-2 + 13x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2 + 13x + -3x2 = 0

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

Divide each side by '-3'.
0.6666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -4.333333333x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -4.333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -4.333333333x + x2 = 0 + -0.6666666667
-4.333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-4.333333333x + x2 = -0.6666666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -0.6666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -0.6666666667 + 4.694444446

Combine like terms: -0.6666666667 + 4.694444446 = 4.0277777793
4.694444446 + -4.333333333x + x2 = 4.0277777793

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 4.0277777793

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 2.00693243 and -2.00693243.


Subproblem 1
x + -2.166666667 = 2.00693243

Simplifying
x + -2.166666667 = 2.00693243

Reorder the terms:
-2.166666667 + x = 2.00693243

Solving
-2.166666667 + x = 2.00693243

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 2.00693243 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 2.00693243 + 2.166666667
x = 2.00693243 + 2.166666667

Combine like terms: 2.00693243 + 2.166666667 = 4.173599097
x = 4.173599097

Simplifying
x = 4.173599097


Subproblem 2
x + -2.166666667 = -2.00693243

Simplifying
x + -2.166666667 = -2.00693243

Reorder the terms:
-2.166666667 + x = -2.00693243

Solving
-2.166666667 + x = -2.00693243

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -2.00693243 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -2.00693243 + 2.166666667
x = -2.00693243 + 2.166666667

Combine like terms: -2.00693243 + 2.166666667 = 0.159734237
x = 0.159734237

Simplifying
x = 0.159734237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.173599097, 0.159734237}

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