(Y*y)+y=0

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Solution for (Y*y)+y=0 equation: 


Simplifying
(Y * y) + y = 0

Multiply Y * y
(yY) + y = 0
yY + y = 0

Reorder the terms:
y + yY = 0

Solving
y + yY = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + Y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(1 + Y)' equal to zero and attempt to solve:

Simplifying
1 + Y = 0

Solving
1 + Y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + Y = 0 + -1
Y = 0 + -1

Combine like terms: 0 + -1 = -1
Y = -1

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

Combine like terms: Y + -1Y = 0
0 = -1 + -1Y

Simplifying
0 = -1 + -1Y

The solution to this equation could not be determined.

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

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