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

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


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

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

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

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

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) + x(x + -3) = (x + -3)(x + 5)

Reorder the terms:
-15 + -2x + x2 + x(-3 + x) = (x + -3)(x + 5)
-15 + -2x + x2 + (-3 * x + x * x) = (x + -3)(x + 5)
-15 + -2x + x2 + (-3x + x2) = (x + -3)(x + 5)

Reorder the terms:
-15 + -2x + -3x + x2 + x2 = (x + -3)(x + 5)

Combine like terms: -2x + -3x = -5x
-15 + -5x + x2 + x2 = (x + -3)(x + 5)

Combine like terms: x2 + x2 = 2x2
-15 + -5x + 2x2 = (x + -3)(x + 5)

Reorder the terms:
-15 + -5x + 2x2 = (-3 + x)(x + 5)

Reorder the terms:
-15 + -5x + 2x2 = (-3 + x)(5 + x)

Multiply (-3 + x) * (5 + x)
-15 + -5x + 2x2 = (-3(5 + x) + x(5 + x))
-15 + -5x + 2x2 = ((5 * -3 + x * -3) + x(5 + x))
-15 + -5x + 2x2 = ((-15 + -3x) + x(5 + x))
-15 + -5x + 2x2 = (-15 + -3x + (5 * x + x * x))
-15 + -5x + 2x2 = (-15 + -3x + (5x + x2))

Combine like terms: -3x + 5x = 2x
-15 + -5x + 2x2 = (-15 + 2x + x2)

Add '15' to each side of the equation.
-15 + -5x + 15 + 2x2 = -15 + 2x + 15 + x2

Reorder the terms:
-15 + 15 + -5x + 2x2 = -15 + 2x + 15 + x2

Combine like terms: -15 + 15 = 0
0 + -5x + 2x2 = -15 + 2x + 15 + x2
-5x + 2x2 = -15 + 2x + 15 + x2

Reorder the terms:
-5x + 2x2 = -15 + 15 + 2x + x2

Combine like terms: -15 + 15 = 0
-5x + 2x2 = 0 + 2x + x2
-5x + 2x2 = 2x + x2

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

Solving for variable 'x'.

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

Combine like terms: -5x + -2x = -7x
-7x + 2x2 + -1x2 = 2x + x2 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-7x + 1x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
-7x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-7x + 1x2 = 0 + x2 + -1x2
-7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + x) = 0


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 '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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