3x(y-13)=5xy(2)

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Solution for 3x(y-13)=5xy(2) equation: 


Simplifying
3x(y + -13) = 5xy(2)

Reorder the terms:
3x(-13 + y) = 5xy(2)
(-13 * 3x + y * 3x) = 5xy(2)
(-39x + 3xy) = 5xy(2)

Reorder the terms for easier multiplication:
-39x + 3xy = 5 * 2xy

Multiply 5 * 2
-39x + 3xy = 10xy

Solving
-39x + 3xy = 10xy

Solving for variable 'x'.

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

Add '-10xy' to each side of the equation.
-39x + 3xy + -10xy = 10xy + -10xy

Combine like terms: 3xy + -10xy = -7xy
-39x + -7xy = 10xy + -10xy

Combine like terms: 10xy + -10xy = 0
-39x + -7xy = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(39 + 7y) = 0

Ignore the factor -1.

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 '(39 + 7y)' equal to zero and attempt to solve:

Simplifying
39 + 7y = 0

Solving
39 + 7y = 0

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

Add '-39' to each side of the equation.
39 + -39 + 7y = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 7y = 0 + -39
7y = 0 + -39

Combine like terms: 0 + -39 = -39
7y = -39

Add '-7y' to each side of the equation.
7y + -7y = -39 + -7y

Combine like terms: 7y + -7y = 0
0 = -39 + -7y

Simplifying
0 = -39 + -7y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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