7(x-1)6x+1=12-3(x-4)

Solution for 7(x-1)6x+1=12-3(x-4) equation:

Simplifying
7(x + -1) * 6x + 1 = 12 + -3(x + -4)

Reorder the terms:
7(-1 + x) * 6x + 1 = 12 + -3(x + -4)

Reorder the terms for easier multiplication:
7 * 6x(-1 + x) + 1 = 12 + -3(x + -4)

Multiply 7 * 6
42x(-1 + x) + 1 = 12 + -3(x + -4)
(-1 * 42x + x * 42x) + 1 = 12 + -3(x + -4)
(-42x + 42x2) + 1 = 12 + -3(x + -4)

Reorder the terms:
1 + -42x + 42x2 = 12 + -3(x + -4)

Reorder the terms:
1 + -42x + 42x2 = 12 + -3(-4 + x)
1 + -42x + 42x2 = 12 + (-4 * -3 + x * -3)
1 + -42x + 42x2 = 12 + (12 + -3x)

Combine like terms: 12 + 12 = 24
1 + -42x + 42x2 = 24 + -3x

Solving
1 + -42x + 42x2 = 24 + -3x

Solving for variable 'x'.

Reorder the terms:
1 + -24 + -42x + 3x + 42x2 = 24 + -3x + -24 + 3x

Combine like terms: 1 + -24 = -23
-23 + -42x + 3x + 42x2 = 24 + -3x + -24 + 3x

Combine like terms: -42x + 3x = -39x
-23 + -39x + 42x2 = 24 + -3x + -24 + 3x

Reorder the terms:
-23 + -39x + 42x2 = 24 + -24 + -3x + 3x

Combine like terms: 24 + -24 = 0
-23 + -39x + 42x2 = 0 + -3x + 3x
-23 + -39x + 42x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-23 + -39x + 42x2 = 0

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

Divide each side by '42'.
-0.5476190476 + -0.9285714286x + x2 = 0

Move the constant term to the right:

Add '0.5476190476' to each side of the equation.
-0.5476190476 + -0.9285714286x + 0.5476190476 + x2 = 0 + 0.5476190476

Reorder the terms:
-0.5476190476 + 0.5476190476 + -0.9285714286x + x2 = 0 + 0.5476190476

Combine like terms: -0.5476190476 + 0.5476190476 = 0.0000000000
0.0000000000 + -0.9285714286x + x2 = 0 + 0.5476190476
-0.9285714286x + x2 = 0 + 0.5476190476

Combine like terms: 0 + 0.5476190476 = 0.5476190476
-0.9285714286x + x2 = 0.5476190476

The x term is -0.9285714286x.  Take half its coefficient (-0.4642857143).
Square it (0.2155612245) and add it to both sides.

Add '0.2155612245' to each side of the equation.
-0.9285714286x + 0.2155612245 + x2 = 0.5476190476 + 0.2155612245

Reorder the terms:
0.2155612245 + -0.9285714286x + x2 = 0.5476190476 + 0.2155612245

Combine like terms: 0.5476190476 + 0.2155612245 = 0.7631802721
0.2155612245 + -0.9285714286x + x2 = 0.7631802721

Factor a perfect square on the left side:
(x + -0.4642857143)(x + -0.4642857143) = 0.7631802721

Calculate the square root of the right side: 0.873601896

Break this problem into two subproblems by setting 
(x + -0.4642857143) equal to 0.873601896 and -0.873601896.

Subproblem 1
x + -0.4642857143 = 0.873601896

Simplifying
x + -0.4642857143 = 0.873601896

Reorder the terms:
-0.4642857143 + x = 0.873601896

Solving
-0.4642857143 + x = 0.873601896

Solving for variable 'x'.

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

Add '0.4642857143' to each side of the equation.
-0.4642857143 + 0.4642857143 + x = 0.873601896 + 0.4642857143

Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000
0.0000000000 + x = 0.873601896 + 0.4642857143
x = 0.873601896 + 0.4642857143

Combine like terms: 0.873601896 + 0.4642857143 = 1.3378876103
x = 1.3378876103

Simplifying
x = 1.3378876103

Subproblem 2
x + -0.4642857143 = -0.873601896

Simplifying
x + -0.4642857143 = -0.873601896

Reorder the terms:
-0.4642857143 + x = -0.873601896

Solving
-0.4642857143 + x = -0.873601896

Solving for variable 'x'.

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

Add '0.4642857143' to each side of the equation.
-0.4642857143 + 0.4642857143 + x = -0.873601896 + 0.4642857143

Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000
0.0000000000 + x = -0.873601896 + 0.4642857143
x = -0.873601896 + 0.4642857143

Combine like terms: -0.873601896 + 0.4642857143 = -0.4093161817
x = -0.4093161817

Simplifying
x = -0.4093161817

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3378876103, -0.4093161817}