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

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


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

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

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

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

Reorder the terms:
3xy + 3x2 = (2xy + -10x2)
3xy + 3x2 = (2xy + -10x2)

Solving
3xy + 3x2 = 2xy + -10x2

Solving for variable 'x'.

Reorder the terms:
3xy + -2xy + 3x2 + 10x2 = 2xy + -10x2 + -2xy + 10x2

Combine like terms: 3xy + -2xy = 1xy
1xy + 3x2 + 10x2 = 2xy + -10x2 + -2xy + 10x2

Combine like terms: 3x2 + 10x2 = 13x2
1xy + 13x2 = 2xy + -10x2 + -2xy + 10x2

Reorder the terms:
1xy + 13x2 = 2xy + -2xy + -10x2 + 10x2

Combine like terms: 2xy + -2xy = 0
1xy + 13x2 = 0 + -10x2 + 10x2
1xy + 13x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
1xy + 13x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(y + 13x) = 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 '(y + 13x)' equal to zero and attempt to solve:

Simplifying
y + 13x = 0

Reorder the terms:
13x + y = 0

Solving
13x + y = 0

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

Add '-1y' to each side of the equation.
13x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
13x + 0 = 0 + -1y
13x = 0 + -1y
Remove the zero:
13x = -1y

Divide each side by '13'.
x = -0.07692307692y

Simplifying
x = -0.07692307692y
Solution
x = {0, -0.07692307692y}

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