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

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

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

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

Reorder the terms for easier multiplication:
2(5 + x) + -3x = (x + -5)(x + -5)
(5 * 2 + x * 2) + -3x = (x + -5)(x + -5)
(10 + 2x) + -3x = (x + -5)(x + -5)

Combine like terms: 2x + -3x = -1x
10 + -1x = (x + -5)(x + -5)

Reorder the terms:
10 + -1x = (-5 + x)(x + -5)

Reorder the terms:
10 + -1x = (-5 + x)(-5 + x)

Multiply (-5 + x) * (-5 + x)
10 + -1x = (-5(-5 + x) + x(-5 + x))
10 + -1x = ((-5 * -5 + x * -5) + x(-5 + x))
10 + -1x = ((25 + -5x) + x(-5 + x))
10 + -1x = (25 + -5x + (-5 * x + x * x))
10 + -1x = (25 + -5x + (-5x + x2))

Combine like terms: -5x + -5x = -10x
10 + -1x = (25 + -10x + x2)

Solving
10 + -1x = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -25 + -1x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 10 + -25 = -15
-15 + -1x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -1x + 10x = 9x
-15 + 9x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-15 + 9x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-15 + 9x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-15 + 9x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-15 + 9x + -1x2 = 0 + x2 + -1x2
-15 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
15 + -9x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -9x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -9x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -9x + x2 = 0 + -15
-9x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-9x + x2 = -15

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -15 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + -9x + x2 = 5.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + -4.5 = 2.291287847

Simplifying
x + -4.5 = 2.291287847

Reorder the terms:
-4.5 + x = 2.291287847

Solving
-4.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 2.291287847 + 4.5
x = 2.291287847 + 4.5

Combine like terms: 2.291287847 + 4.5 = 6.791287847
x = 6.791287847

Simplifying
x = 6.791287847

Subproblem 2
x + -4.5 = -2.291287847

Simplifying
x + -4.5 = -2.291287847

Reorder the terms:
-4.5 + x = -2.291287847

Solving
-4.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -2.291287847 + 4.5
x = -2.291287847 + 4.5

Combine like terms: -2.291287847 + 4.5 = 2.208712153
x = 2.208712153

Simplifying
x = 2.208712153

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.791287847, 2.208712153}