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

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

Simplifying
2x2 + -5x + 2 = (x + -3)(x + -2) + -13x

Reorder the terms:
2 + -5x + 2x2 = (x + -3)(x + -2) + -13x

Reorder the terms:
2 + -5x + 2x2 = (-3 + x)(x + -2) + -13x

Reorder the terms:
2 + -5x + 2x2 = (-3 + x)(-2 + x) + -13x

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

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

Reorder the terms:
2 + -5x + 2x2 = 6 + -5x + -13x + x2

Combine like terms: -5x + -13x = -18x
2 + -5x + 2x2 = 6 + -18x + x2

Solving
2 + -5x + 2x2 = 6 + -18x + x2

Solving for variable 'x'.

Reorder the terms:
2 + -6 + -5x + 18x + 2x2 + -1x2 = 6 + -18x + x2 + -6 + 18x + -1x2

Combine like terms: 2 + -6 = -4
-4 + -5x + 18x + 2x2 + -1x2 = 6 + -18x + x2 + -6 + 18x + -1x2

Combine like terms: -5x + 18x = 13x
-4 + 13x + 2x2 + -1x2 = 6 + -18x + x2 + -6 + 18x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + 13x + 1x2 = 6 + -18x + x2 + -6 + 18x + -1x2

Reorder the terms:
-4 + 13x + 1x2 = 6 + -6 + -18x + 18x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-4 + 13x + 1x2 = 0 + -18x + 18x + x2 + -1x2
-4 + 13x + 1x2 = -18x + 18x + x2 + -1x2

Combine like terms: -18x + 18x = 0
-4 + 13x + 1x2 = 0 + x2 + -1x2
-4 + 13x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 13x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 13x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 13x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 13x + x2 = 0 + 4
13x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
13x + x2 = 4

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 4 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 4 + 42.25

Combine like terms: 4 + 42.25 = 46.25
42.25 + 13x + x2 = 46.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.800735254 and -6.800735254.

Subproblem 1
x + 6.5 = 6.800735254

Simplifying
x + 6.5 = 6.800735254

Reorder the terms:
6.5 + x = 6.800735254

Solving
6.5 + x = 6.800735254

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.800735254 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.800735254 + -6.5
x = 6.800735254 + -6.5

Combine like terms: 6.800735254 + -6.5 = 0.300735254
x = 0.300735254

Simplifying
x = 0.300735254

Subproblem 2
x + 6.5 = -6.800735254

Simplifying
x + 6.5 = -6.800735254

Reorder the terms:
6.5 + x = -6.800735254

Solving
6.5 + x = -6.800735254

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.800735254 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.800735254 + -6.5
x = -6.800735254 + -6.5

Combine like terms: -6.800735254 + -6.5 = -13.300735254
x = -13.300735254

Simplifying
x = -13.300735254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.300735254, -13.300735254}