(x-3).6(x+1)=65

Solution for (x-3).6(x+1)=65 equation:

Simplifying
(x + -3) * 0.6(x + 1) = 65

Reorder the terms:
(-3 + x) * 0.6(x + 1) = 65

Reorder the terms:
(-3 + x) * 0.6(1 + x) = 65

Reorder the terms for easier multiplication:
0.6(-3 + x)(1 + x) = 65

Multiply (-3 + x) * (1 + x)
0.6(-3(1 + x) + x(1 + x)) = 65
0.6((1 * -3 + x * -3) + x(1 + x)) = 65
0.6((-3 + -3x) + x(1 + x)) = 65
0.6(-3 + -3x + (1 * x + x * x)) = 65
0.6(-3 + -3x + (1x + x2)) = 65

Combine like terms: -3x + 1x = -2x
0.6(-3 + -2x + x2) = 65
(-3 * 0.6 + -2x * 0.6 + x2 * 0.6) = 65
(-1.8 + -1.2x + 0.6x2) = 65

Solving
-1.8 + -1.2x + 0.6x2 = 65

Solving for variable 'x'.

Reorder the terms:
-1.8 + -65 + -1.2x + 0.6x2 = 65 + -65

Combine like terms: -1.8 + -65 = -66.8
-66.8 + -1.2x + 0.6x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-66.8 + -1.2x + 0.6x2 = 0

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

Divide each side by '0.6'.
-111.3333333 + -2x + x2 = 0

Move the constant term to the right:

Add '111.3333333' to each side of the equation.
-111.3333333 + -2x + 111.3333333 + x2 = 0 + 111.3333333

Reorder the terms:
-111.3333333 + 111.3333333 + -2x + x2 = 0 + 111.3333333

Combine like terms: -111.3333333 + 111.3333333 = 0.0000000
0.0000000 + -2x + x2 = 0 + 111.3333333
-2x + x2 = 0 + 111.3333333

Combine like terms: 0 + 111.3333333 = 111.3333333
-2x + x2 = 111.3333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 111.3333333 + 1

Reorder the terms:
1 + -2x + x2 = 111.3333333 + 1

Combine like terms: 111.3333333 + 1 = 112.3333333
1 + -2x + x2 = 112.3333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 112.3333333

Calculate the square root of the right side: 10.598742062

Break this problem into two subproblems by setting 
(x + -1) equal to 10.598742062 and -10.598742062.

Subproblem 1
x + -1 = 10.598742062

Simplifying
x + -1 = 10.598742062

Reorder the terms:
-1 + x = 10.598742062

Solving
-1 + x = 10.598742062

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 10.598742062 + 1

Combine like terms: -1 + 1 = 0
0 + x = 10.598742062 + 1
x = 10.598742062 + 1

Combine like terms: 10.598742062 + 1 = 11.598742062
x = 11.598742062

Simplifying
x = 11.598742062

Subproblem 2
x + -1 = -10.598742062

Simplifying
x + -1 = -10.598742062

Reorder the terms:
-1 + x = -10.598742062

Solving
-1 + x = -10.598742062

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -10.598742062 + 1

Combine like terms: -1 + 1 = 0
0 + x = -10.598742062 + 1
x = -10.598742062 + 1

Combine like terms: -10.598742062 + 1 = -9.598742062
x = -9.598742062

Simplifying
x = -9.598742062

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.598742062, -9.598742062}