(x-2)(x+3)=13x-5

Solution for (x-2)(x+3)=13x-5 equation:

Simplifying
(x + -2)(x + 3) = 13x + -5

Reorder the terms:
(-2 + x)(x + 3) = 13x + -5

Reorder the terms:
(-2 + x)(3 + x) = 13x + -5

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = 13x + -5
((3 * -2 + x * -2) + x(3 + x)) = 13x + -5
((-6 + -2x) + x(3 + x)) = 13x + -5
(-6 + -2x + (3 * x + x * x)) = 13x + -5
(-6 + -2x + (3x + x2)) = 13x + -5

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = 13x + -5

Reorder the terms:
-6 + 1x + x2 = -5 + 13x

Solving
-6 + 1x + x2 = -5 + 13x

Solving for variable 'x'.

Reorder the terms:
-6 + 5 + 1x + -13x + x2 = -5 + 13x + 5 + -13x

Combine like terms: -6 + 5 = -1
-1 + 1x + -13x + x2 = -5 + 13x + 5 + -13x

Combine like terms: 1x + -13x = -12x
-1 + -12x + x2 = -5 + 13x + 5 + -13x

Reorder the terms:
-1 + -12x + x2 = -5 + 5 + 13x + -13x

Combine like terms: -5 + 5 = 0
-1 + -12x + x2 = 0 + 13x + -13x
-1 + -12x + x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-1 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -12x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -12x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12x + x2 = 0 + 1
-12x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-12x + x2 = 1

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 1 + 36

Reorder the terms:
36 + -12x + x2 = 1 + 36

Combine like terms: 1 + 36 = 37
36 + -12x + x2 = 37

Factor a perfect square on the left side:
(x + -6)(x + -6) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -6) equal to 6.08276253 and -6.08276253.

Subproblem 1
x + -6 = 6.08276253

Simplifying
x + -6 = 6.08276253

Reorder the terms:
-6 + x = 6.08276253

Solving
-6 + x = 6.08276253

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 6.08276253 + 6

Combine like terms: -6 + 6 = 0
0 + x = 6.08276253 + 6
x = 6.08276253 + 6

Combine like terms: 6.08276253 + 6 = 12.08276253
x = 12.08276253

Simplifying
x = 12.08276253

Subproblem 2
x + -6 = -6.08276253

Simplifying
x + -6 = -6.08276253

Reorder the terms:
-6 + x = -6.08276253

Solving
-6 + x = -6.08276253

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -6.08276253 + 6

Combine like terms: -6 + 6 = 0
0 + x = -6.08276253 + 6
x = -6.08276253 + 6

Combine like terms: -6.08276253 + 6 = -0.08276253
x = -0.08276253

Simplifying
x = -0.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.08276253, -0.08276253}