(2x+3)(3x)=86

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Solution for (2x+3)(3x)=86 equation: 


Simplifying
(2x + 3)(3x) = 86

Reorder the terms:
(3 + 2x)(3x) = 86

Remove parenthesis around (3x)
(3 + 2x) * 3x = 86

Reorder the terms for easier multiplication:
3x(3 + 2x) = 86
(3 * 3x + 2x * 3x) = 86
(9x + 6x2) = 86

Solving
9x + 6x2 = 86

Solving for variable 'x'.

Reorder the terms:
-86 + 9x + 6x2 = 86 + -86

Combine like terms: 86 + -86 = 0
-86 + 9x + 6x2 = 0

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

Divide each side by '6'.
-14.33333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '14.33333333' to each side of the equation.
-14.33333333 + 1.5x + 14.33333333 + x2 = 0 + 14.33333333

Reorder the terms:
-14.33333333 + 14.33333333 + 1.5x + x2 = 0 + 14.33333333

Combine like terms: -14.33333333 + 14.33333333 = 0.00000000
0.00000000 + 1.5x + x2 = 0 + 14.33333333
1.5x + x2 = 0 + 14.33333333

Combine like terms: 0 + 14.33333333 = 14.33333333
1.5x + x2 = 14.33333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 14.33333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 14.33333333 + 0.5625

Combine like terms: 14.33333333 + 0.5625 = 14.89583333
0.5625 + 1.5x + x2 = 14.89583333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 14.89583333

Calculate the square root of the right side: 3.859512059

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.859512059 and -3.859512059.


Subproblem 1
x + 0.75 = 3.859512059

Simplifying
x + 0.75 = 3.859512059

Reorder the terms:
0.75 + x = 3.859512059

Solving
0.75 + x = 3.859512059

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.859512059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.859512059 + -0.75
x = 3.859512059 + -0.75

Combine like terms: 3.859512059 + -0.75 = 3.109512059
x = 3.109512059

Simplifying
x = 3.109512059


Subproblem 2
x + 0.75 = -3.859512059

Simplifying
x + 0.75 = -3.859512059

Reorder the terms:
0.75 + x = -3.859512059

Solving
0.75 + x = -3.859512059

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.859512059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.859512059 + -0.75
x = -3.859512059 + -0.75

Combine like terms: -3.859512059 + -0.75 = -4.609512059
x = -4.609512059

Simplifying
x = -4.609512059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.109512059, -4.609512059}

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