2y^2+8y-6=y^2+6y+9

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Solution for 2y^2+8y-6=y^2+6y+9 equation: 


Simplifying
2y2 + 8y + -6 = y2 + 6y + 9

Reorder the terms:
-6 + 8y + 2y2 = y2 + 6y + 9

Reorder the terms:
-6 + 8y + 2y2 = 9 + 6y + y2

Solving
-6 + 8y + 2y2 = 9 + 6y + y2

Solving for variable 'y'.

Reorder the terms:
-6 + -9 + 8y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: -6 + -9 = -15
-15 + 8y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 8y + -6y = 2y
-15 + 2y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-15 + 2y + 1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Reorder the terms:
-15 + 2y + 1y2 = 9 + -9 + 6y + -6y + y2 + -1y2

Combine like terms: 9 + -9 = 0
-15 + 2y + 1y2 = 0 + 6y + -6y + y2 + -1y2
-15 + 2y + 1y2 = 6y + -6y + y2 + -1y2

Combine like terms: 6y + -6y = 0
-15 + 2y + 1y2 = 0 + y2 + -1y2
-15 + 2y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + 2y + 1y2 = 0

Factor a trinomial.
(-5 + -1y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5, 3}

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