3(x-1)+6=-6x(x+7)

Solution for 3(x-1)+6=-6x(x+7) equation:

Simplifying
3(x + -1) + 6 = -6x(x + 7)

Reorder the terms:
3(-1 + x) + 6 = -6x(x + 7)
(-1 * 3 + x * 3) + 6 = -6x(x + 7)
(-3 + 3x) + 6 = -6x(x + 7)

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

Combine like terms: -3 + 6 = 3
3 + 3x = -6x(x + 7)

Reorder the terms:
3 + 3x = -6x(7 + x)
3 + 3x = (7 * -6x + x * -6x)
3 + 3x = (-42x + -6x2)

Solving
3 + 3x = -42x + -6x2

Solving for variable 'x'.

Combine like terms: 3x + 42x = 45x
3 + 45x + 6x2 = -42x + -6x2 + 42x + 6x2

Reorder the terms:
3 + 45x + 6x2 = -42x + 42x + -6x2 + 6x2

Combine like terms: -42x + 42x = 0
3 + 45x + 6x2 = 0 + -6x2 + 6x2
3 + 45x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
3 + 45x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 15x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 15x + 2x2 = 0

Solving
1 + 15x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 7.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 7.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 7.5x + x2 = 0 + -0.5
7.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
7.5x + x2 = -0.5

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -0.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -0.5 + 14.0625

Combine like terms: -0.5 + 14.0625 = 13.5625
14.0625 + 7.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.682729966 and -3.682729966.

Subproblem 1
x + 3.75 = 3.682729966

Simplifying
x + 3.75 = 3.682729966

Reorder the terms:
3.75 + x = 3.682729966

Solving
3.75 + x = 3.682729966

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.682729966 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.682729966 + -3.75
x = 3.682729966 + -3.75

Combine like terms: 3.682729966 + -3.75 = -0.067270034
x = -0.067270034

Simplifying
x = -0.067270034

Subproblem 2
x + 3.75 = -3.682729966

Simplifying
x + 3.75 = -3.682729966

Reorder the terms:
3.75 + x = -3.682729966

Solving
3.75 + x = -3.682729966

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.682729966 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.682729966 + -3.75
x = -3.682729966 + -3.75

Combine like terms: -3.682729966 + -3.75 = -7.432729966
x = -7.432729966

Simplifying
x = -7.432729966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.067270034, -7.432729966}
Solution
x = {-0.067270034, -7.432729966}