3x(y+5)=2x(y-8)

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Solution for 3x(y+5)=2x(y-8) equation: 


Simplifying
3x(y + 5) = 2x(y + -8)

Reorder the terms:
3x(5 + y) = 2x(y + -8)
(5 * 3x + y * 3x) = 2x(y + -8)
(15x + 3xy) = 2x(y + -8)

Reorder the terms:
15x + 3xy = 2x(-8 + y)
15x + 3xy = (-8 * 2x + y * 2x)
15x + 3xy = (-16x + 2xy)

Solving
15x + 3xy = -16x + 2xy

Solving for variable 'x'.

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

Add '16x' to each side of the equation.
15x + 16x + 3xy = -16x + 16x + 2xy

Combine like terms: 15x + 16x = 31x
31x + 3xy = -16x + 16x + 2xy

Combine like terms: -16x + 16x = 0
31x + 3xy = 0 + 2xy
31x + 3xy = 2xy

Add '-2xy' to each side of the equation.
31x + 3xy + -2xy = 2xy + -2xy

Combine like terms: 3xy + -2xy = 1xy
31x + 1xy = 2xy + -2xy

Combine like terms: 2xy + -2xy = 0
31x + 1xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(31 + y) = 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 '(31 + y)' equal to zero and attempt to solve:

Simplifying
31 + y = 0

Solving
31 + y = 0

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

Add '-31' to each side of the equation.
31 + -31 + y = 0 + -31

Combine like terms: 31 + -31 = 0
0 + y = 0 + -31
y = 0 + -31

Combine like terms: 0 + -31 = -31
y = -31

Add '-1y' to each side of the equation.
y + -1y = -31 + -1y

Combine like terms: y + -1y = 0
0 = -31 + -1y

Simplifying
0 = -31 + -1y

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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