2y^2+10y+9=y^2+6y+9

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Solution for 2y^2+10y+9=y^2+6y+9 equation: 


Simplifying
2y2 + 10y + 9 = y2 + 6y + 9

Reorder the terms:
9 + 10y + 2y2 = y2 + 6y + 9

Reorder the terms:
9 + 10y + 2y2 = 9 + 6y + y2

Add '-9' to each side of the equation.
9 + 10y + -9 + 2y2 = 9 + 6y + -9 + y2

Reorder the terms:
9 + -9 + 10y + 2y2 = 9 + 6y + -9 + y2

Combine like terms: 9 + -9 = 0
0 + 10y + 2y2 = 9 + 6y + -9 + y2
10y + 2y2 = 9 + 6y + -9 + y2

Reorder the terms:
10y + 2y2 = 9 + -9 + 6y + y2

Combine like terms: 9 + -9 = 0
10y + 2y2 = 0 + 6y + y2
10y + 2y2 = 6y + y2

Solving
10y + 2y2 = 6y + y2

Solving for variable 'y'.

Reorder the terms:
10y + -6y + 2y2 + -1y2 = 6y + y2 + -6y + -1y2

Combine like terms: 10y + -6y = 4y
4y + 2y2 + -1y2 = 6y + y2 + -6y + -1y2

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

Reorder the terms:
4y + 1y2 = 6y + -6y + y2 + -1y2

Combine like terms: 6y + -6y = 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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