3(2x+4)8x=-2(x+1)+3

Solution for 3(2x+4)8x=-2(x+1)+3 equation:

Simplifying
3(2x + 4) * 8x = -2(x + 1) + 3

Reorder the terms:
3(4 + 2x) * 8x = -2(x + 1) + 3

Reorder the terms for easier multiplication:
3 * 8x(4 + 2x) = -2(x + 1) + 3

Multiply 3 * 8
24x(4 + 2x) = -2(x + 1) + 3
(4 * 24x + 2x * 24x) = -2(x + 1) + 3
(96x + 48x2) = -2(x + 1) + 3

Reorder the terms:
96x + 48x2 = -2(1 + x) + 3
96x + 48x2 = (1 * -2 + x * -2) + 3
96x + 48x2 = (-2 + -2x) + 3

Reorder the terms:
96x + 48x2 = -2 + 3 + -2x

Combine like terms: -2 + 3 = 1
96x + 48x2 = 1 + -2x

Solving
96x + 48x2 = 1 + -2x

Solving for variable 'x'.

Reorder the terms:
-1 + 96x + 2x + 48x2 = 1 + -2x + -1 + 2x

Combine like terms: 96x + 2x = 98x
-1 + 98x + 48x2 = 1 + -2x + -1 + 2x

Reorder the terms:
-1 + 98x + 48x2 = 1 + -1 + -2x + 2x

Combine like terms: 1 + -1 = 0
-1 + 98x + 48x2 = 0 + -2x + 2x
-1 + 98x + 48x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-1 + 98x + 48x2 = 0

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

Divide each side by '48'.
-0.02083333333 + 2.041666667x + x2 = 0

Move the constant term to the right:

Add '0.02083333333' to each side of the equation.
-0.02083333333 + 2.041666667x + 0.02083333333 + x2 = 0 + 0.02083333333

Reorder the terms:
-0.02083333333 + 0.02083333333 + 2.041666667x + x2 = 0 + 0.02083333333

Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000
0.00000000000 + 2.041666667x + x2 = 0 + 0.02083333333
2.041666667x + x2 = 0 + 0.02083333333

Combine like terms: 0 + 0.02083333333 = 0.02083333333
2.041666667x + x2 = 0.02083333333

The x term is 2.041666667x.  Take half its coefficient (1.020833334).
Square it (1.042100696) and add it to both sides.

Add '1.042100696' to each side of the equation.
2.041666667x + 1.042100696 + x2 = 0.02083333333 + 1.042100696

Reorder the terms:
1.042100696 + 2.041666667x + x2 = 0.02083333333 + 1.042100696

Combine like terms: 0.02083333333 + 1.042100696 = 1.06293402933
1.042100696 + 2.041666667x + x2 = 1.06293402933

Factor a perfect square on the left side:
(x + 1.020833334)(x + 1.020833334) = 1.06293402933

Calculate the square root of the right side: 1.03098692

Break this problem into two subproblems by setting 
(x + 1.020833334) equal to 1.03098692 and -1.03098692.

Subproblem 1
x + 1.020833334 = 1.03098692

Simplifying
x + 1.020833334 = 1.03098692

Reorder the terms:
1.020833334 + x = 1.03098692

Solving
1.020833334 + x = 1.03098692

Solving for variable 'x'.

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

Add '-1.020833334' to each side of the equation.
1.020833334 + -1.020833334 + x = 1.03098692 + -1.020833334

Combine like terms: 1.020833334 + -1.020833334 = 0.000000000
0.000000000 + x = 1.03098692 + -1.020833334
x = 1.03098692 + -1.020833334

Combine like terms: 1.03098692 + -1.020833334 = 0.010153586
x = 0.010153586

Simplifying
x = 0.010153586

Subproblem 2
x + 1.020833334 = -1.03098692

Simplifying
x + 1.020833334 = -1.03098692

Reorder the terms:
1.020833334 + x = -1.03098692

Solving
1.020833334 + x = -1.03098692

Solving for variable 'x'.

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

Add '-1.020833334' to each side of the equation.
1.020833334 + -1.020833334 + x = -1.03098692 + -1.020833334

Combine like terms: 1.020833334 + -1.020833334 = 0.000000000
0.000000000 + x = -1.03098692 + -1.020833334
x = -1.03098692 + -1.020833334

Combine like terms: -1.03098692 + -1.020833334 = -2.051820254
x = -2.051820254

Simplifying
x = -2.051820254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.010153586, -2.051820254}