y^2+6y+11=2y^2+9y-17

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Solution for y^2+6y+11=2y^2+9y-17 equation: 


Simplifying
y2 + 6y + 11 = 2y2 + 9y + -17

Reorder the terms:
11 + 6y + y2 = 2y2 + 9y + -17

Reorder the terms:
11 + 6y + y2 = -17 + 9y + 2y2

Solving
11 + 6y + y2 = -17 + 9y + 2y2

Solving for variable 'y'.

Reorder the terms:
11 + 17 + 6y + -9y + y2 + -2y2 = -17 + 9y + 2y2 + 17 + -9y + -2y2

Combine like terms: 11 + 17 = 28
28 + 6y + -9y + y2 + -2y2 = -17 + 9y + 2y2 + 17 + -9y + -2y2

Combine like terms: 6y + -9y = -3y
28 + -3y + y2 + -2y2 = -17 + 9y + 2y2 + 17 + -9y + -2y2

Combine like terms: y2 + -2y2 = -1y2
28 + -3y + -1y2 = -17 + 9y + 2y2 + 17 + -9y + -2y2

Reorder the terms:
28 + -3y + -1y2 = -17 + 17 + 9y + -9y + 2y2 + -2y2

Combine like terms: -17 + 17 = 0
28 + -3y + -1y2 = 0 + 9y + -9y + 2y2 + -2y2
28 + -3y + -1y2 = 9y + -9y + 2y2 + -2y2

Combine like terms: 9y + -9y = 0
28 + -3y + -1y2 = 0 + 2y2 + -2y2
28 + -3y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
28 + -3y + -1y2 = 0

Factor a trinomial.
(4 + -1y)(7 + y) = 0


Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4

Subproblem 2
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7
Solution
y = {4, -7}

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