2[3x-1]4[x+2]=84

Solution for 2[3x-1]4[x+2]=84 equation:

Simplifying
2[3x + -1] * 4[x + 2] = 84

Reorder the terms:
2[-1 + 3x] * 4[x + 2] = 84

Reorder the terms:
2[-1 + 3x] * 4[2 + x] = 84

Reorder the terms for easier multiplication:
2 * 4[-1 + 3x][2 + x] = 84

Multiply 2 * 4
8[-1 + 3x][2 + x] = 84

Multiply [-1 + 3x] * [2 + x]
8[-1[2 + x] + 3x * [2 + x]] = 84
8[[2 * -1 + x * -1] + 3x * [2 + x]] = 84
8[[-2 + -1x] + 3x * [2 + x]] = 84
8[-2 + -1x + [2 * 3x + x * 3x]] = 84
8[-2 + -1x + [6x + 3x2]] = 84

Combine like terms: -1x + 6x = 5x
8[-2 + 5x + 3x2] = 84
[-2 * 8 + 5x * 8 + 3x2 * 8] = 84
[-16 + 40x + 24x2] = 84

Solving
-16 + 40x + 24x2 = 84

Solving for variable 'x'.

Reorder the terms:
-16 + -84 + 40x + 24x2 = 84 + -84

Combine like terms: -16 + -84 = -100
-100 + 40x + 24x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-100 + 40x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 10x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-25 + 10x + 6x2)' equal to zero and attempt to solve:

Simplifying
-25 + 10x + 6x2 = 0

Solving
-25 + 10x + 6x2 = 0

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

Divide each side by '6'.
-4.166666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 1.666666667x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 1.666666667x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 4.166666667
1.666666667x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
1.666666667x + x2 = 4.166666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 4.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 4.166666667 + 0.6944444447

Combine like terms: 4.166666667 + 0.6944444447 = 4.8611111117
0.6944444447 + 1.666666667x + x2 = 4.8611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 4.8611111117

Calculate the square root of the right side: 2.204792759

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.204792759 and -2.204792759.

Subproblem 1
x + 0.8333333335 = 2.204792759

Simplifying
x + 0.8333333335 = 2.204792759

Reorder the terms:
0.8333333335 + x = 2.204792759

Solving
0.8333333335 + x = 2.204792759

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.204792759 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.204792759 + -0.8333333335
x = 2.204792759 + -0.8333333335

Combine like terms: 2.204792759 + -0.8333333335 = 1.3714594255
x = 1.3714594255

Simplifying
x = 1.3714594255

Subproblem 2
x + 0.8333333335 = -2.204792759

Simplifying
x + 0.8333333335 = -2.204792759

Reorder the terms:
0.8333333335 + x = -2.204792759

Solving
0.8333333335 + x = -2.204792759

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.204792759 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.204792759 + -0.8333333335
x = -2.204792759 + -0.8333333335

Combine like terms: -2.204792759 + -0.8333333335 = -3.0381260925
x = -3.0381260925

Simplifying
x = -3.0381260925

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3714594255, -3.0381260925}
Solution
x = {1.3714594255, -3.0381260925}