y^2+2y+1=14y-31

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Solution for y^2+2y+1=14y-31 equation: 


Simplifying
y2 + 2y + 1 = 14y + -31

Reorder the terms:
1 + 2y + y2 = 14y + -31

Reorder the terms:
1 + 2y + y2 = -31 + 14y

Solving
1 + 2y + y2 = -31 + 14y

Solving for variable 'y'.

Reorder the terms:
1 + 31 + 2y + -14y + y2 = -31 + 14y + 31 + -14y

Combine like terms: 1 + 31 = 32
32 + 2y + -14y + y2 = -31 + 14y + 31 + -14y

Combine like terms: 2y + -14y = -12y
32 + -12y + y2 = -31 + 14y + 31 + -14y

Reorder the terms:
32 + -12y + y2 = -31 + 31 + 14y + -14y

Combine like terms: -31 + 31 = 0
32 + -12y + y2 = 0 + 14y + -14y
32 + -12y + y2 = 14y + -14y

Combine like terms: 14y + -14y = 0
32 + -12y + y2 = 0

Factor a trinomial.
(4 + -1y)(8 + -1y) = 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 '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {4, 8}

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