3(4x+7)*2x=3-2(x-1)

Solution for 3(4x+7)*2x=3-2(x-1) equation:

Simplifying
3(4x + 7) * 2x = 3 + -2(x + -1)

Reorder the terms:
3(7 + 4x) * 2x = 3 + -2(x + -1)

Reorder the terms for easier multiplication:
3 * 2x(7 + 4x) = 3 + -2(x + -1)

Multiply 3 * 2
6x(7 + 4x) = 3 + -2(x + -1)
(7 * 6x + 4x * 6x) = 3 + -2(x + -1)
(42x + 24x2) = 3 + -2(x + -1)

Reorder the terms:
42x + 24x2 = 3 + -2(-1 + x)
42x + 24x2 = 3 + (-1 * -2 + x * -2)
42x + 24x2 = 3 + (2 + -2x)

Combine like terms: 3 + 2 = 5
42x + 24x2 = 5 + -2x

Solving
42x + 24x2 = 5 + -2x

Solving for variable 'x'.

Reorder the terms:
-5 + 42x + 2x + 24x2 = 5 + -2x + -5 + 2x

Combine like terms: 42x + 2x = 44x
-5 + 44x + 24x2 = 5 + -2x + -5 + 2x

Reorder the terms:
-5 + 44x + 24x2 = 5 + -5 + -2x + 2x

Combine like terms: 5 + -5 = 0
-5 + 44x + 24x2 = 0 + -2x + 2x
-5 + 44x + 24x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-5 + 44x + 24x2 = 0

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

Divide each side by '24'.
-0.2083333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + 1.833333333x + 0.2083333333 + x2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + 1.833333333x + x2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + 1.833333333x + x2 = 0 + 0.2083333333
1.833333333x + x2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
1.833333333x + x2 = 0.2083333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 0.2083333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 0.2083333333 + 0.8402777775

Combine like terms: 0.2083333333 + 0.8402777775 = 1.0486111108
0.8402777775 + 1.833333333x + x2 = 1.0486111108

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 1.0486111108

Calculate the square root of the right side: 1.024017144

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 1.024017144 and -1.024017144.

Subproblem 1
x + 0.9166666665 = 1.024017144

Simplifying
x + 0.9166666665 = 1.024017144

Reorder the terms:
0.9166666665 + x = 1.024017144

Solving
0.9166666665 + x = 1.024017144

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 1.024017144 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 1.024017144 + -0.9166666665
x = 1.024017144 + -0.9166666665

Combine like terms: 1.024017144 + -0.9166666665 = 0.1073504775
x = 0.1073504775

Simplifying
x = 0.1073504775

Subproblem 2
x + 0.9166666665 = -1.024017144

Simplifying
x + 0.9166666665 = -1.024017144

Reorder the terms:
0.9166666665 + x = -1.024017144

Solving
0.9166666665 + x = -1.024017144

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -1.024017144 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -1.024017144 + -0.9166666665
x = -1.024017144 + -0.9166666665

Combine like terms: -1.024017144 + -0.9166666665 = -1.9406838105
x = -1.9406838105

Simplifying
x = -1.9406838105

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1073504775, -1.9406838105}