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

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

Simplifying
(x + -3)(x + -3) + (x + -5)(x + 5) = 0

Reorder the terms:
(-3 + x)(x + -3) + (x + -5)(x + 5) = 0

Reorder the terms:
(-3 + x)(-3 + x) + (x + -5)(x + 5) = 0

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) + (x + -5)(x + 5) = 0
((-3 * -3 + x * -3) + x(-3 + x)) + (x + -5)(x + 5) = 0
((9 + -3x) + x(-3 + x)) + (x + -5)(x + 5) = 0
(9 + -3x + (-3 * x + x * x)) + (x + -5)(x + 5) = 0
(9 + -3x + (-3x + x2)) + (x + -5)(x + 5) = 0

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) + (x + -5)(x + 5) = 0

Reorder the terms:
9 + -6x + x2 + (-5 + x)(x + 5) = 0

Reorder the terms:
9 + -6x + x2 + (-5 + x)(5 + x) = 0

Multiply (-5 + x) * (5 + x)
9 + -6x + x2 + (-5(5 + x) + x(5 + x)) = 0
9 + -6x + x2 + ((5 * -5 + x * -5) + x(5 + x)) = 0
9 + -6x + x2 + ((-25 + -5x) + x(5 + x)) = 0
9 + -6x + x2 + (-25 + -5x + (5 * x + x * x)) = 0
9 + -6x + x2 + (-25 + -5x + (5x + x2)) = 0

Combine like terms: -5x + 5x = 0
9 + -6x + x2 + (-25 + 0 + x2) = 0
9 + -6x + x2 + (-25 + x2) = 0

Reorder the terms:
9 + -25 + -6x + x2 + x2 = 0

Combine like terms: 9 + -25 = -16
-16 + -6x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-16 + -6x + 2x2 = 0

Solving
-16 + -6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + -3x + x2 = 0

Solving
-8 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -3x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x + x2 = 0 + 8
-3x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3x + x2 = 8

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 8 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3x + x2 = 10.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + -1.5 = 3.201562119

Simplifying
x + -1.5 = 3.201562119

Reorder the terms:
-1.5 + x = 3.201562119

Solving
-1.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.201562119 + 1.5
x = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
x = 4.701562119

Simplifying
x = 4.701562119

Subproblem 2
x + -1.5 = -3.201562119

Simplifying
x + -1.5 = -3.201562119

Reorder the terms:
-1.5 + x = -3.201562119

Solving
-1.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.201562119 + 1.5
x = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
x = -1.701562119

Simplifying
x = -1.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.701562119, -1.701562119}
Solution
x = {4.701562119, -1.701562119}