12(4x)-28x(x-1)=21(x+1)

Solution for 12(4x)-28x(x-1)=21(x+1) equation:

Simplifying
12(4x) + -28x(x + -1) = 21(x + 1)

Remove parenthesis around (4x)
12 * 4x + -28x(x + -1) = 21(x + 1)

Multiply 12 * 4
48x + -28x(x + -1) = 21(x + 1)

Reorder the terms:
48x + -28x(-1 + x) = 21(x + 1)
48x + (-1 * -28x + x * -28x) = 21(x + 1)
48x + (28x + -28x2) = 21(x + 1)

Combine like terms: 48x + 28x = 76x
76x + -28x2 = 21(x + 1)

Reorder the terms:
76x + -28x2 = 21(1 + x)
76x + -28x2 = (1 * 21 + x * 21)
76x + -28x2 = (21 + 21x)

Solving
76x + -28x2 = 21 + 21x

Solving for variable 'x'.

Reorder the terms:
-21 + 76x + -21x + -28x2 = 21 + 21x + -21 + -21x

Combine like terms: 76x + -21x = 55x
-21 + 55x + -28x2 = 21 + 21x + -21 + -21x

Reorder the terms:
-21 + 55x + -28x2 = 21 + -21 + 21x + -21x

Combine like terms: 21 + -21 = 0
-21 + 55x + -28x2 = 0 + 21x + -21x
-21 + 55x + -28x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-21 + 55x + -28x2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
0.75 + -1.964285714x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -1.964285714x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -1.964285714x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -1.964285714x + x2 = 0 + -0.75
-1.964285714x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-1.964285714x + x2 = -0.75

The x term is -1.964285714x.  Take half its coefficient (-0.982142857).
Square it (0.9646045916) and add it to both sides.

Add '0.9646045916' to each side of the equation.
-1.964285714x + 0.9646045916 + x2 = -0.75 + 0.9646045916

Reorder the terms:
0.9646045916 + -1.964285714x + x2 = -0.75 + 0.9646045916

Combine like terms: -0.75 + 0.9646045916 = 0.2146045916
0.9646045916 + -1.964285714x + x2 = 0.2146045916

Factor a perfect square on the left side:
(x + -0.982142857)(x + -0.982142857) = 0.2146045916

Calculate the square root of the right side: 0.463254349

Break this problem into two subproblems by setting 
(x + -0.982142857) equal to 0.463254349 and -0.463254349.

Subproblem 1
x + -0.982142857 = 0.463254349

Simplifying
x + -0.982142857 = 0.463254349

Reorder the terms:
-0.982142857 + x = 0.463254349

Solving
-0.982142857 + x = 0.463254349

Solving for variable 'x'.

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

Add '0.982142857' to each side of the equation.
-0.982142857 + 0.982142857 + x = 0.463254349 + 0.982142857

Combine like terms: -0.982142857 + 0.982142857 = 0.000000000
0.000000000 + x = 0.463254349 + 0.982142857
x = 0.463254349 + 0.982142857

Combine like terms: 0.463254349 + 0.982142857 = 1.445397206
x = 1.445397206

Simplifying
x = 1.445397206

Subproblem 2
x + -0.982142857 = -0.463254349

Simplifying
x + -0.982142857 = -0.463254349

Reorder the terms:
-0.982142857 + x = -0.463254349

Solving
-0.982142857 + x = -0.463254349

Solving for variable 'x'.

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

Add '0.982142857' to each side of the equation.
-0.982142857 + 0.982142857 + x = -0.463254349 + 0.982142857

Combine like terms: -0.982142857 + 0.982142857 = 0.000000000
0.000000000 + x = -0.463254349 + 0.982142857
x = -0.463254349 + 0.982142857

Combine like terms: -0.463254349 + 0.982142857 = 0.518888508
x = 0.518888508

Simplifying
x = 0.518888508

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.445397206, 0.518888508}