3x(x+5)-x(x+6)=2

Solution for 3x(x+5)-x(x+6)=2 equation:

Simplifying
3x(x + 5) + -1x(x + 6) = 2

Reorder the terms:
3x(5 + x) + -1x(x + 6) = 2
(5 * 3x + x * 3x) + -1x(x + 6) = 2
(15x + 3x2) + -1x(x + 6) = 2

Reorder the terms:
15x + 3x2 + -1x(6 + x) = 2
15x + 3x2 + (6 * -1x + x * -1x) = 2
15x + 3x2 + (-6x + -1x2) = 2

Reorder the terms:
15x + -6x + 3x2 + -1x2 = 2

Combine like terms: 15x + -6x = 9x
9x + 3x2 + -1x2 = 2

Combine like terms: 3x2 + -1x2 = 2x2
9x + 2x2 = 2

Solving
9x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 9x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 9x + 2x2 = 0

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

Divide each side by '2'.
-1 + 4.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4.5x + x2 = 0 + 1
4.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4.5x + x2 = 1

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 1 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 1 + 5.0625

Combine like terms: 1 + 5.0625 = 6.0625
5.0625 + 4.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.46221445 and -2.46221445.

Subproblem 1
x + 2.25 = 2.46221445

Simplifying
x + 2.25 = 2.46221445

Reorder the terms:
2.25 + x = 2.46221445

Solving
2.25 + x = 2.46221445

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.46221445 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.46221445 + -2.25
x = 2.46221445 + -2.25

Combine like terms: 2.46221445 + -2.25 = 0.21221445
x = 0.21221445

Simplifying
x = 0.21221445

Subproblem 2
x + 2.25 = -2.46221445

Simplifying
x + 2.25 = -2.46221445

Reorder the terms:
2.25 + x = -2.46221445

Solving
2.25 + x = -2.46221445

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.46221445 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.46221445 + -2.25
x = -2.46221445 + -2.25

Combine like terms: -2.46221445 + -2.25 = -4.71221445
x = -4.71221445

Simplifying
x = -4.71221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.21221445, -4.71221445}