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

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Solution for (x-3)x(x+1)=(x-5)x(x+5) equation: 


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

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

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

Reorder the terms for easier multiplication:
x(-3 + x)(1 + x) = (x + -5) * x(x + 5)

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

Combine like terms: -3x + 1x = -2x
x(-3 + -2x + x2) = (x + -5) * x(x + 5)
(-3 * x + -2x * x + x2 * x) = (x + -5) * x(x + 5)
(-3x + -2x2 + x3) = (x + -5) * x(x + 5)

Reorder the terms:
-3x + -2x2 + x3 = (-5 + x) * x(x + 5)

Reorder the terms:
-3x + -2x2 + x3 = (-5 + x) * x(5 + x)

Reorder the terms for easier multiplication:
-3x + -2x2 + x3 = x(-5 + x)(5 + x)

Multiply (-5 + x) * (5 + x)
-3x + -2x2 + x3 = x(-5(5 + x) + x(5 + x))
-3x + -2x2 + x3 = x((5 * -5 + x * -5) + x(5 + x))
-3x + -2x2 + x3 = x((-25 + -5x) + x(5 + x))
-3x + -2x2 + x3 = x(-25 + -5x + (5 * x + x * x))
-3x + -2x2 + x3 = x(-25 + -5x + (5x + x2))

Combine like terms: -5x + 5x = 0
-3x + -2x2 + x3 = x(-25 + 0 + x2)
-3x + -2x2 + x3 = x(-25 + x2)
-3x + -2x2 + x3 = (-25 * x + x2 * x)
-3x + -2x2 + x3 = (-25x + x3)

Add '-1x3' to each side of the equation.
-3x + -2x2 + x3 + -1x3 = -25x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-3x + -2x2 + 0 = -25x + x3 + -1x3
-3x + -2x2 = -25x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-3x + -2x2 = -25x + 0
-3x + -2x2 = -25x

Solving
-3x + -2x2 = -25x

Solving for variable 'x'.

Reorder the terms:
-3x + 25x + -2x2 = -25x + 25x

Combine like terms: -3x + 25x = 22x
22x + -2x2 = -25x + 25x

Combine like terms: -25x + 25x = 0
22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {0, 11}

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