2(x-6)=3x(x+7)

Solution for 2(x-6)=3x(x+7) equation:

Simplifying
2(x + -6) = 3x(x + 7)

Reorder the terms:
2(-6 + x) = 3x(x + 7)
(-6 * 2 + x * 2) = 3x(x + 7)
(-12 + 2x) = 3x(x + 7)

Reorder the terms:
-12 + 2x = 3x(7 + x)
-12 + 2x = (7 * 3x + x * 3x)
-12 + 2x = (21x + 3x2)

Solving
-12 + 2x = 21x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + -21x = -19x
-12 + -19x + -3x2 = 21x + 3x2 + -21x + -3x2

Reorder the terms:
-12 + -19x + -3x2 = 21x + -21x + 3x2 + -3x2

Combine like terms: 21x + -21x = 0
-12 + -19x + -3x2 = 0 + 3x2 + -3x2
-12 + -19x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12 + -19x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 19x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + 19x + 3x2)' equal to zero and attempt to solve:

Simplifying
12 + 19x + 3x2 = 0

Solving
12 + 19x + 3x2 = 0

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

Divide each side by '3'.
4 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 6.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6.333333333x + x2 = 0 + -4
6.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
6.333333333x + x2 = -4

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 = -4 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = -4 + 10.02777778

Combine like terms: -4 + 10.02777778 = 6.02777778
10.02777778 + 6.333333333x + x2 = 6.02777778

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 6.02777778

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 2.455153311 and -2.455153311.

Subproblem 1
x + 3.166666667 = 2.455153311

Simplifying
x + 3.166666667 = 2.455153311

Reorder the terms:
3.166666667 + x = 2.455153311

Solving
3.166666667 + x = 2.455153311

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 = 2.455153311 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 2.455153311 + -3.166666667
x = 2.455153311 + -3.166666667

Combine like terms: 2.455153311 + -3.166666667 = -0.711513356
x = -0.711513356

Simplifying
x = -0.711513356

Subproblem 2
x + 3.166666667 = -2.455153311

Simplifying
x + 3.166666667 = -2.455153311

Reorder the terms:
3.166666667 + x = -2.455153311

Solving
3.166666667 + x = -2.455153311

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 = -2.455153311 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -2.455153311 + -3.166666667
x = -2.455153311 + -3.166666667

Combine like terms: -2.455153311 + -3.166666667 = -5.621819978
x = -5.621819978

Simplifying
x = -5.621819978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.711513356, -5.621819978}
Solution
x = {-0.711513356, -5.621819978}