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

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

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

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

Combine like terms: -6 + 5 = -1
-1 + 2x + -1x = 3(x + 5)(x + -3)

Combine like terms: 2x + -1x = 1x
-1 + 1x = 3(x + 5)(x + -3)

Reorder the terms:
-1 + 1x = 3(5 + x)(x + -3)

Reorder the terms:
-1 + 1x = 3(5 + x)(-3 + x)

Multiply (5 + x) * (-3 + x)
-1 + 1x = 3(5(-3 + x) + x(-3 + x))
-1 + 1x = 3((-3 * 5 + x * 5) + x(-3 + x))
-1 + 1x = 3((-15 + 5x) + x(-3 + x))
-1 + 1x = 3(-15 + 5x + (-3 * x + x * x))
-1 + 1x = 3(-15 + 5x + (-3x + x2))

Combine like terms: 5x + -3x = 2x
-1 + 1x = 3(-15 + 2x + x2)
-1 + 1x = (-15 * 3 + 2x * 3 + x2 * 3)
-1 + 1x = (-45 + 6x + 3x2)

Solving
-1 + 1x = -45 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
-1 + 45 + 1x + -6x + -3x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Combine like terms: -1 + 45 = 44
44 + 1x + -6x + -3x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Combine like terms: 1x + -6x = -5x
44 + -5x + -3x2 = -45 + 6x + 3x2 + 45 + -6x + -3x2

Reorder the terms:
44 + -5x + -3x2 = -45 + 45 + 6x + -6x + 3x2 + -3x2

Combine like terms: -45 + 45 = 0
44 + -5x + -3x2 = 0 + 6x + -6x + 3x2 + -3x2
44 + -5x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
44 + -5x + -3x2 = 0 + 3x2 + -3x2
44 + -5x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
44 + -5x + -3x2 = 0

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

Divide each side by '-3'.
-14.66666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '14.66666667' to each side of the equation.
-14.66666667 + 1.666666667x + 14.66666667 + x2 = 0 + 14.66666667

Reorder the terms:
-14.66666667 + 14.66666667 + 1.666666667x + x2 = 0 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + 1.666666667x + x2 = 0 + 14.66666667
1.666666667x + x2 = 0 + 14.66666667

Combine like terms: 0 + 14.66666667 = 14.66666667
1.666666667x + x2 = 14.66666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 14.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 14.66666667 + 0.6944444447

Combine like terms: 14.66666667 + 0.6944444447 = 15.3611111147
0.6944444447 + 1.666666667x + x2 = 15.3611111147

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 15.3611111147

Calculate the square root of the right side: 3.919325339

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 3.919325339 and -3.919325339.

Subproblem 1
x + 0.8333333335 = 3.919325339

Simplifying
x + 0.8333333335 = 3.919325339

Reorder the terms:
0.8333333335 + x = 3.919325339

Solving
0.8333333335 + x = 3.919325339

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 3.919325339 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 3.919325339 + -0.8333333335
x = 3.919325339 + -0.8333333335

Combine like terms: 3.919325339 + -0.8333333335 = 3.0859920055
x = 3.0859920055

Simplifying
x = 3.0859920055

Subproblem 2
x + 0.8333333335 = -3.919325339

Simplifying
x + 0.8333333335 = -3.919325339

Reorder the terms:
0.8333333335 + x = -3.919325339

Solving
0.8333333335 + x = -3.919325339

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -3.919325339 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -3.919325339 + -0.8333333335
x = -3.919325339 + -0.8333333335

Combine like terms: -3.919325339 + -0.8333333335 = -4.7526586725
x = -4.7526586725

Simplifying
x = -4.7526586725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.0859920055, -4.7526586725}