(3x+3)(2x)=146

Solution for (3x+3)(2x)=146 equation:

Simplifying
(3x + 3)(2x) = 146

Reorder the terms:
(3 + 3x)(2x) = 146

Remove parenthesis around (2x)
(3 + 3x) * 2x = 146

Reorder the terms for easier multiplication:
2x(3 + 3x) = 146
(3 * 2x + 3x * 2x) = 146
(6x + 6x2) = 146

Solving
6x + 6x2 = 146

Solving for variable 'x'.

Reorder the terms:
-146 + 6x + 6x2 = 146 + -146

Combine like terms: 146 + -146 = 0
-146 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-73 + 3x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-73 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-73 + 3x + 3x2 = 0

Solving
-73 + 3x + 3x2 = 0

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

Divide each side by '3'.
-24.33333333 + x + x2 = 0

Move the constant term to the right:

Add '24.33333333' to each side of the equation.
-24.33333333 + x + 24.33333333 + x2 = 0 + 24.33333333

Reorder the terms:
-24.33333333 + 24.33333333 + x + x2 = 0 + 24.33333333

Combine like terms: -24.33333333 + 24.33333333 = 0.00000000
0.00000000 + x + x2 = 0 + 24.33333333
x + x2 = 0 + 24.33333333

Combine like terms: 0 + 24.33333333 = 24.33333333
x + x2 = 24.33333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 24.33333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 24.33333333 + 0.25

Combine like terms: 24.33333333 + 0.25 = 24.58333333
1.25 + x2 = 24.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 24.58333333

Calculate the square root of the right side: 4.95815826

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.95815826 and -4.95815826.

Subproblem 1
x + 0.5 = 4.95815826

Simplifying
x + 0.5 = 4.95815826

Reorder the terms:
0.5 + x = 4.95815826

Solving
0.5 + x = 4.95815826

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.95815826 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.95815826 + -0.5
x = 4.95815826 + -0.5

Combine like terms: 4.95815826 + -0.5 = 4.45815826
x = 4.45815826

Simplifying
x = 4.45815826

Subproblem 2
x + 0.5 = -4.95815826

Simplifying
x + 0.5 = -4.95815826

Reorder the terms:
0.5 + x = -4.95815826

Solving
0.5 + x = -4.95815826

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.95815826 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.95815826 + -0.5
x = -4.95815826 + -0.5

Combine like terms: -4.95815826 + -0.5 = -5.45815826
x = -5.45815826

Simplifying
x = -5.45815826

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.45815826, -5.45815826}
Solution
x = {4.45815826, -5.45815826}