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

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

Simplifying
3x + -4(x2 + -6 + -7) = 6(x + -7)

Reorder the terms:
3x + -4(-6 + -7 + x2) = 6(x + -7)

Combine like terms: -6 + -7 = -13
3x + -4(-13 + x2) = 6(x + -7)
3x + (-13 * -4 + x2 * -4) = 6(x + -7)
3x + (52 + -4x2) = 6(x + -7)

Reorder the terms:
52 + 3x + -4x2 = 6(x + -7)

Reorder the terms:
52 + 3x + -4x2 = 6(-7 + x)
52 + 3x + -4x2 = (-7 * 6 + x * 6)
52 + 3x + -4x2 = (-42 + 6x)

Solving
52 + 3x + -4x2 = -42 + 6x

Solving for variable 'x'.

Reorder the terms:
52 + 42 + 3x + -6x + -4x2 = -42 + 6x + 42 + -6x

Combine like terms: 52 + 42 = 94
94 + 3x + -6x + -4x2 = -42 + 6x + 42 + -6x

Combine like terms: 3x + -6x = -3x
94 + -3x + -4x2 = -42 + 6x + 42 + -6x

Reorder the terms:
94 + -3x + -4x2 = -42 + 42 + 6x + -6x

Combine like terms: -42 + 42 = 0
94 + -3x + -4x2 = 0 + 6x + -6x
94 + -3x + -4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
94 + -3x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-23.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '23.5' to each side of the equation.
-23.5 + 0.75x + 23.5 + x2 = 0 + 23.5

Reorder the terms:
-23.5 + 23.5 + 0.75x + x2 = 0 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + 0.75x + x2 = 0 + 23.5
0.75x + x2 = 0 + 23.5

Combine like terms: 0 + 23.5 = 23.5
0.75x + x2 = 23.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 23.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 23.5 + 0.140625

Combine like terms: 23.5 + 0.140625 = 23.640625
0.140625 + 0.75x + x2 = 23.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 23.640625

Calculate the square root of the right side: 4.862162585

Break this problem into two subproblems by setting 
(x + 0.375) equal to 4.862162585 and -4.862162585.

Subproblem 1
x + 0.375 = 4.862162585

Simplifying
x + 0.375 = 4.862162585

Reorder the terms:
0.375 + x = 4.862162585

Solving
0.375 + x = 4.862162585

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 4.862162585 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 4.862162585 + -0.375
x = 4.862162585 + -0.375

Combine like terms: 4.862162585 + -0.375 = 4.487162585
x = 4.487162585

Simplifying
x = 4.487162585

Subproblem 2
x + 0.375 = -4.862162585

Simplifying
x + 0.375 = -4.862162585

Reorder the terms:
0.375 + x = -4.862162585

Solving
0.375 + x = -4.862162585

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -4.862162585 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -4.862162585 + -0.375
x = -4.862162585 + -0.375

Combine like terms: -4.862162585 + -0.375 = -5.237162585
x = -5.237162585

Simplifying
x = -5.237162585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.487162585, -5.237162585}