(y+5)x(y+1)=(y+10)x(y-3)

Solution for (y+5)x(y+1)=(y+10)x(y-3) equation:

Simplifying
(y + 5) * x(y + 1) = (y + 10) * x(y + -3)

Reorder the terms:
(5 + y) * x(y + 1) = (y + 10) * x(y + -3)

Reorder the terms:
(5 + y) * x(1 + y) = (y + 10) * x(y + -3)

Reorder the terms for easier multiplication:
x(5 + y)(1 + y) = (y + 10) * x(y + -3)

Multiply (5 + y) * (1 + y)
x(5(1 + y) + y(1 + y)) = (y + 10) * x(y + -3)
x((1 * 5 + y * 5) + y(1 + y)) = (y + 10) * x(y + -3)
x((5 + 5y) + y(1 + y)) = (y + 10) * x(y + -3)
x(5 + 5y + (1 * y + y * y)) = (y + 10) * x(y + -3)
x(5 + 5y + (1y + y2)) = (y + 10) * x(y + -3)

Combine like terms: 5y + 1y = 6y
x(5 + 6y + y2) = (y + 10) * x(y + -3)
(5 * x + 6y * x + y2 * x) = (y + 10) * x(y + -3)
(5x + 6xy + xy2) = (y + 10) * x(y + -3)

Reorder the terms:
5x + 6xy + xy2 = (10 + y) * x(y + -3)

Reorder the terms:
5x + 6xy + xy2 = (10 + y) * x(-3 + y)

Reorder the terms for easier multiplication:
5x + 6xy + xy2 = x(10 + y)(-3 + y)

Multiply (10 + y) * (-3 + y)
5x + 6xy + xy2 = x(10(-3 + y) + y(-3 + y))
5x + 6xy + xy2 = x((-3 * 10 + y * 10) + y(-3 + y))
5x + 6xy + xy2 = x((-30 + 10y) + y(-3 + y))
5x + 6xy + xy2 = x(-30 + 10y + (-3 * y + y * y))
5x + 6xy + xy2 = x(-30 + 10y + (-3y + y2))

Combine like terms: 10y + -3y = 7y
5x + 6xy + xy2 = x(-30 + 7y + y2)
5x + 6xy + xy2 = (-30 * x + 7y * x + y2 * x)
5x + 6xy + xy2 = (-30x + 7xy + xy2)

Add '-1xy2' to each side of the equation.
5x + 6xy + xy2 + -1xy2 = -30x + 7xy + xy2 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
5x + 6xy + 0 = -30x + 7xy + xy2 + -1xy2
5x + 6xy = -30x + 7xy + xy2 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
5x + 6xy = -30x + 7xy + 0
5x + 6xy = -30x + 7xy

Solving
5x + 6xy = -30x + 7xy

Solving for variable 'x'.

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

Add '30x' to each side of the equation.
5x + 30x + 6xy = -30x + 30x + 7xy

Combine like terms: 5x + 30x = 35x
35x + 6xy = -30x + 30x + 7xy

Combine like terms: -30x + 30x = 0
35x + 6xy = 0 + 7xy
35x + 6xy = 7xy

Add '-7xy' to each side of the equation.
35x + 6xy + -7xy = 7xy + -7xy

Combine like terms: 6xy + -7xy = -1xy
35x + -1xy = 7xy + -7xy

Combine like terms: 7xy + -7xy = 0
35x + -1xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(35 + -1y) = 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 '(35 + -1y)' equal to zero and attempt to solve:

Simplifying
35 + -1y = 0

Solving
35 + -1y = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1y = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1y = 0 + -35
-1y = 0 + -35

Combine like terms: 0 + -35 = -35
-1y = -35

Add 'y' to each side of the equation.
-1y + y = -35 + y

Combine like terms: -1y + y = 0
0 = -35 + y

Simplifying
0 = -35 + y

The solution to this equation could not be determined.

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