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

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

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

Reorder the terms:
6(-3 + x) + (x + 3) = 5(x + 3)(x + -3)
(-3 * 6 + x * 6) + (x + 3) = 5(x + 3)(x + -3)
(-18 + 6x) + (x + 3) = 5(x + 3)(x + -3)

Reorder the terms:
-18 + 6x + (3 + x) = 5(x + 3)(x + -3)

Remove parenthesis around (3 + x)
-18 + 6x + 3 + x = 5(x + 3)(x + -3)

Reorder the terms:
-18 + 3 + 6x + x = 5(x + 3)(x + -3)

Combine like terms: -18 + 3 = -15
-15 + 6x + x = 5(x + 3)(x + -3)

Combine like terms: 6x + x = 7x
-15 + 7x = 5(x + 3)(x + -3)

Reorder the terms:
-15 + 7x = 5(3 + x)(x + -3)

Reorder the terms:
-15 + 7x = 5(3 + x)(-3 + x)

Multiply (3 + x) * (-3 + x)
-15 + 7x = 5(3(-3 + x) + x(-3 + x))
-15 + 7x = 5((-3 * 3 + x * 3) + x(-3 + x))
-15 + 7x = 5((-9 + 3x) + x(-3 + x))
-15 + 7x = 5(-9 + 3x + (-3 * x + x * x))
-15 + 7x = 5(-9 + 3x + (-3x + x2))

Combine like terms: 3x + -3x = 0
-15 + 7x = 5(-9 + 0 + x2)
-15 + 7x = 5(-9 + x2)
-15 + 7x = (-9 * 5 + x2 * 5)
-15 + 7x = (-45 + 5x2)

Solving
-15 + 7x = -45 + 5x2

Solving for variable 'x'.

Reorder the terms:
-15 + 45 + 7x + -5x2 = -45 + 5x2 + 45 + -5x2

Combine like terms: -15 + 45 = 30
30 + 7x + -5x2 = -45 + 5x2 + 45 + -5x2

Reorder the terms:
30 + 7x + -5x2 = -45 + 45 + 5x2 + -5x2

Combine like terms: -45 + 45 = 0
30 + 7x + -5x2 = 0 + 5x2 + -5x2
30 + 7x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
30 + 7x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-6 + -1.4x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -1.4x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -1.4x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1.4x + x2 = 0 + 6
-1.4x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1.4x + x2 = 6

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 6 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 6 + 0.49

Combine like terms: 6 + 0.49 = 6.49
0.49 + -1.4x + x2 = 6.49

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 6.49

Calculate the square root of the right side: 2.547547841

Break this problem into two subproblems by setting 
(x + -0.7) equal to 2.547547841 and -2.547547841.

Subproblem 1
x + -0.7 = 2.547547841

Simplifying
x + -0.7 = 2.547547841

Reorder the terms:
-0.7 + x = 2.547547841

Solving
-0.7 + x = 2.547547841

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 2.547547841 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 2.547547841 + 0.7
x = 2.547547841 + 0.7

Combine like terms: 2.547547841 + 0.7 = 3.247547841
x = 3.247547841

Simplifying
x = 3.247547841

Subproblem 2
x + -0.7 = -2.547547841

Simplifying
x + -0.7 = -2.547547841

Reorder the terms:
-0.7 + x = -2.547547841

Solving
-0.7 + x = -2.547547841

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -2.547547841 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -2.547547841 + 0.7
x = -2.547547841 + 0.7

Combine like terms: -2.547547841 + 0.7 = -1.847547841
x = -1.847547841

Simplifying
x = -1.847547841

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.247547841, -1.847547841}