50*x=75*x(10-x)

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Solution for 50*x=75*x(10-x) equation: 


Simplifying
50x = 75x(10 + -1x)
50x = (10 * 75x + -1x * 75x)
50x = (750x + -75x2)

Solving
50x = 750x + -75x2

Solving for variable 'x'.

Combine like terms: 50x + -750x = -700x
-700x + 75x2 = 750x + -75x2 + -750x + 75x2

Reorder the terms:
-700x + 75x2 = 750x + -750x + -75x2 + 75x2

Combine like terms: 750x + -750x = 0
-700x + 75x2 = 0 + -75x2 + 75x2
-700x + 75x2 = -75x2 + 75x2

Combine like terms: -75x2 + 75x2 = 0
-700x + 75x2 = 0

Factor out the Greatest Common Factor (GCF), '25x'.
25x(-28 + 3x) = 0

Ignore the factor 25.

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 '(-28 + 3x)' equal to zero and attempt to solve:

Simplifying
-28 + 3x = 0

Solving
-28 + 3x = 0

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

Add '28' to each side of the equation.
-28 + 28 + 3x = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 3x = 0 + 28
3x = 0 + 28

Combine like terms: 0 + 28 = 28
3x = 28

Divide each side by '3'.
x = 9.333333333

Simplifying
x = 9.333333333
Solution
x = {0, 9.333333333}

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