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

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


Simplifying
(5 + -1x)(x + -3) + -1(x + 3)(x + -5) = 0

Reorder the terms:
(5 + -1x)(-3 + x) + -1(x + 3)(x + -5) = 0

Multiply (5 + -1x) * (-3 + x)
(5(-3 + x) + -1x * (-3 + x)) + -1(x + 3)(x + -5) = 0
((-3 * 5 + x * 5) + -1x * (-3 + x)) + -1(x + 3)(x + -5) = 0
((-15 + 5x) + -1x * (-3 + x)) + -1(x + 3)(x + -5) = 0
(-15 + 5x + (-3 * -1x + x * -1x)) + -1(x + 3)(x + -5) = 0
(-15 + 5x + (3x + -1x2)) + -1(x + 3)(x + -5) = 0

Combine like terms: 5x + 3x = 8x
(-15 + 8x + -1x2) + -1(x + 3)(x + -5) = 0

Reorder the terms:
-15 + 8x + -1x2 + -1(3 + x)(x + -5) = 0

Reorder the terms:
-15 + 8x + -1x2 + -1(3 + x)(-5 + x) = 0

Multiply (3 + x) * (-5 + x)
-15 + 8x + -1x2 + -1(3(-5 + x) + x(-5 + x)) = 0
-15 + 8x + -1x2 + -1((-5 * 3 + x * 3) + x(-5 + x)) = 0
-15 + 8x + -1x2 + -1((-15 + 3x) + x(-5 + x)) = 0
-15 + 8x + -1x2 + -1(-15 + 3x + (-5 * x + x * x)) = 0
-15 + 8x + -1x2 + -1(-15 + 3x + (-5x + x2)) = 0

Combine like terms: 3x + -5x = -2x
-15 + 8x + -1x2 + -1(-15 + -2x + x2) = 0
-15 + 8x + -1x2 + (-15 * -1 + -2x * -1 + x2 * -1) = 0
-15 + 8x + -1x2 + (15 + 2x + -1x2) = 0

Reorder the terms:
-15 + 15 + 8x + 2x + -1x2 + -1x2 = 0

Combine like terms: -15 + 15 = 0
0 + 8x + 2x + -1x2 + -1x2 = 0
8x + 2x + -1x2 + -1x2 = 0

Combine like terms: 8x + 2x = 10x
10x + -1x2 + -1x2 = 0

Combine like terms: -1x2 + -1x2 = -2x2
10x + -2x2 = 0

Solving
10x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 5}

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