2y(y+3)=y(y+2)+0

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Solution for 2y(y+3)=y(y+2)+0 equation: 


Simplifying
2y(y + 3) = y(y + 2) + 0

Reorder the terms:
2y(3 + y) = y(y + 2) + 0
(3 * 2y + y * 2y) = y(y + 2) + 0
(6y + 2y2) = y(y + 2) + 0

Reorder the terms:
6y + 2y2 = y(2 + y) + 0
6y + 2y2 = (2 * y + y * y) + 0
6y + 2y2 = (2y + y2) + 0

Reorder the terms:
6y + 2y2 = 0 + 2y + y2
Remove the zero:
6y + 2y2 = 2y + y2

Solving
6y + 2y2 = 2y + y2

Solving for variable 'y'.

Reorder the terms:
6y + -2y + 2y2 + -1y2 = 2y + y2 + -2y + -1y2

Combine like terms: 6y + -2y = 4y
4y + 2y2 + -1y2 = 2y + y2 + -2y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
4y + 1y2 = 2y + y2 + -2y + -1y2

Reorder the terms:
4y + 1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
4y + 1y2 = 0 + y2 + -1y2
4y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
4y + 1y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(4 + 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 '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {0, -4}

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