3(x-6)x+7=-2(x+4)

Solution for 3(x-6)x+7=-2(x+4) equation:

Simplifying
3(x + -6) * x + 7 = -2(x + 4)

Reorder the terms:
3(-6 + x) * x + 7 = -2(x + 4)

Reorder the terms for easier multiplication:
3x(-6 + x) + 7 = -2(x + 4)
(-6 * 3x + x * 3x) + 7 = -2(x + 4)
(-18x + 3x2) + 7 = -2(x + 4)

Reorder the terms:
7 + -18x + 3x2 = -2(x + 4)

Reorder the terms:
7 + -18x + 3x2 = -2(4 + x)
7 + -18x + 3x2 = (4 * -2 + x * -2)
7 + -18x + 3x2 = (-8 + -2x)

Solving
7 + -18x + 3x2 = -8 + -2x

Solving for variable 'x'.

Reorder the terms:
7 + 8 + -18x + 2x + 3x2 = -8 + -2x + 8 + 2x

Combine like terms: 7 + 8 = 15
15 + -18x + 2x + 3x2 = -8 + -2x + 8 + 2x

Combine like terms: -18x + 2x = -16x
15 + -16x + 3x2 = -8 + -2x + 8 + 2x

Reorder the terms:
15 + -16x + 3x2 = -8 + 8 + -2x + 2x

Combine like terms: -8 + 8 = 0
15 + -16x + 3x2 = 0 + -2x + 2x
15 + -16x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
15 + -16x + 3x2 = 0

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

Divide each side by '3'.
5 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5.333333333x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -5.333333333x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5.333333333x + x2 = 0 + -5
-5.333333333x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5.333333333x + x2 = -5

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = -5 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = -5 + 7.111111113

Combine like terms: -5 + 7.111111113 = 2.111111113
7.111111113 + -5.333333333x + x2 = 2.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 2.111111113

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 1.452966315 and -1.452966315.

Subproblem 1
x + -2.666666667 = 1.452966315

Simplifying
x + -2.666666667 = 1.452966315

Reorder the terms:
-2.666666667 + x = 1.452966315

Solving
-2.666666667 + x = 1.452966315

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 1.452966315 + 2.666666667
x = 1.452966315 + 2.666666667

Combine like terms: 1.452966315 + 2.666666667 = 4.119632982
x = 4.119632982

Simplifying
x = 4.119632982

Subproblem 2
x + -2.666666667 = -1.452966315

Simplifying
x + -2.666666667 = -1.452966315

Reorder the terms:
-2.666666667 + x = -1.452966315

Solving
-2.666666667 + x = -1.452966315

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -1.452966315 + 2.666666667
x = -1.452966315 + 2.666666667

Combine like terms: -1.452966315 + 2.666666667 = 1.213700352
x = 1.213700352

Simplifying
x = 1.213700352

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.119632982, 1.213700352}