3(2x-5)x=82

Solution for 3(2x-5)x=82 equation:

Simplifying
3(2x + -5) * x = 82

Reorder the terms:
3(-5 + 2x) * x = 82

Reorder the terms for easier multiplication:
3x(-5 + 2x) = 82
(-5 * 3x + 2x * 3x) = 82
(-15x + 6x2) = 82

Solving
-15x + 6x2 = 82

Solving for variable 'x'.

Reorder the terms:
-82 + -15x + 6x2 = 82 + -82

Combine like terms: 82 + -82 = 0
-82 + -15x + 6x2 = 0

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

Divide each side by '6'.
-13.66666667 + -2.5x + x2 = 0

Move the constant term to the right:

Add '13.66666667' to each side of the equation.
-13.66666667 + -2.5x + 13.66666667 + x2 = 0 + 13.66666667

Reorder the terms:
-13.66666667 + 13.66666667 + -2.5x + x2 = 0 + 13.66666667

Combine like terms: -13.66666667 + 13.66666667 = 0.00000000
0.00000000 + -2.5x + x2 = 0 + 13.66666667
-2.5x + x2 = 0 + 13.66666667

Combine like terms: 0 + 13.66666667 = 13.66666667
-2.5x + x2 = 13.66666667

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 13.66666667 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 13.66666667 + 1.5625

Combine like terms: 13.66666667 + 1.5625 = 15.22916667
1.5625 + -2.5x + x2 = 15.22916667

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 15.22916667

Calculate the square root of the right side: 3.902456492

Break this problem into two subproblems by setting 
(x + -1.25) equal to 3.902456492 and -3.902456492.

Subproblem 1
x + -1.25 = 3.902456492

Simplifying
x + -1.25 = 3.902456492

Reorder the terms:
-1.25 + x = 3.902456492

Solving
-1.25 + x = 3.902456492

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 3.902456492 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 3.902456492 + 1.25
x = 3.902456492 + 1.25

Combine like terms: 3.902456492 + 1.25 = 5.152456492
x = 5.152456492

Simplifying
x = 5.152456492

Subproblem 2
x + -1.25 = -3.902456492

Simplifying
x + -1.25 = -3.902456492

Reorder the terms:
-1.25 + x = -3.902456492

Solving
-1.25 + x = -3.902456492

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -3.902456492 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -3.902456492 + 1.25
x = -3.902456492 + 1.25

Combine like terms: -3.902456492 + 1.25 = -2.652456492
x = -2.652456492

Simplifying
x = -2.652456492

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.152456492, -2.652456492}