(3x+2)(2x)=84

Solution for (3x+2)(2x)=84 equation:

Simplifying
(3x + 2)(2x) = 84

Reorder the terms:
(2 + 3x)(2x) = 84

Remove parenthesis around (2x)
(2 + 3x) * 2x = 84

Reorder the terms for easier multiplication:
2x(2 + 3x) = 84
(2 * 2x + 3x * 2x) = 84
(4x + 6x2) = 84

Solving
4x + 6x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 4x + 6x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 2x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-42 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-42 + 2x + 3x2 = 0

Solving
-42 + 2x + 3x2 = 0

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

Divide each side by '3'.
-14 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 0.6666666667x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 0.6666666667x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 0.6666666667x + x2 = 0 + 14
0.6666666667x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
0.6666666667x + x2 = 14

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 14 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 14 + 0.1111111112

Combine like terms: 14 + 0.1111111112 = 14.1111111112
0.1111111112 + 0.6666666667x + x2 = 14.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 14.1111111112

Calculate the square root of the right side: 3.75647589

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.75647589 and -3.75647589.

Subproblem 1
x + 0.3333333334 = 3.75647589

Simplifying
x + 0.3333333334 = 3.75647589

Reorder the terms:
0.3333333334 + x = 3.75647589

Solving
0.3333333334 + x = 3.75647589

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 3.75647589 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 3.75647589 + -0.3333333334
x = 3.75647589 + -0.3333333334

Combine like terms: 3.75647589 + -0.3333333334 = 3.4231425566
x = 3.4231425566

Simplifying
x = 3.4231425566

Subproblem 2
x + 0.3333333334 = -3.75647589

Simplifying
x + 0.3333333334 = -3.75647589

Reorder the terms:
0.3333333334 + x = -3.75647589

Solving
0.3333333334 + x = -3.75647589

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -3.75647589 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -3.75647589 + -0.3333333334
x = -3.75647589 + -0.3333333334

Combine like terms: -3.75647589 + -0.3333333334 = -4.0898092234
x = -4.0898092234

Simplifying
x = -4.0898092234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4231425566, -4.0898092234}
Solution
x = {3.4231425566, -4.0898092234}