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

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

Simplifying
6(x + -4) = -6 + 6(x2 + -7)

Reorder the terms:
6(-4 + x) = -6 + 6(x2 + -7)
(-4 * 6 + x * 6) = -6 + 6(x2 + -7)
(-24 + 6x) = -6 + 6(x2 + -7)

Reorder the terms:
-24 + 6x = -6 + 6(-7 + x2)
-24 + 6x = -6 + (-7 * 6 + x2 * 6)
-24 + 6x = -6 + (-42 + 6x2)

Combine like terms: -6 + -42 = -48
-24 + 6x = -48 + 6x2

Solving
-24 + 6x = -48 + 6x2

Solving for variable 'x'.

Reorder the terms:
-24 + 48 + 6x + -6x2 = -48 + 6x2 + 48 + -6x2

Combine like terms: -24 + 48 = 24
24 + 6x + -6x2 = -48 + 6x2 + 48 + -6x2

Reorder the terms:
24 + 6x + -6x2 = -48 + 48 + 6x2 + -6x2

Combine like terms: -48 + 48 = 0
24 + 6x + -6x2 = 0 + 6x2 + -6x2
24 + 6x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
24 + 6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + x + -1x2 = 0

Solving
4 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -1x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -1x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x + x2 = 0 + 4
-1x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x + x2 = 4

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

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -1x + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + 0.5 = 2.061552813

Simplifying
x + 0.5 = 2.061552813

Reorder the terms:
0.5 + x = 2.061552813

Solving
0.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.061552813 + -0.5
x = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
x = 1.561552813

Simplifying
x = 1.561552813

Subproblem 2
x + 0.5 = -2.061552813

Simplifying
x + 0.5 = -2.061552813

Reorder the terms:
0.5 + x = -2.061552813

Solving
0.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.061552813 + -0.5
x = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
x = -2.561552813

Simplifying
x = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.561552813, -2.561552813}
Solution
x = {1.561552813, -2.561552813}