2y^2+17y+31=(y+5)(y+5)

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Solution for 2y^2+17y+31=(y+5)(y+5) equation: 


Simplifying
2y2 + 17y + 31 = (y + 5)(y + 5)

Reorder the terms:
31 + 17y + 2y2 = (y + 5)(y + 5)

Reorder the terms:
31 + 17y + 2y2 = (5 + y)(y + 5)

Reorder the terms:
31 + 17y + 2y2 = (5 + y)(5 + y)

Multiply (5 + y) * (5 + y)
31 + 17y + 2y2 = (5(5 + y) + y(5 + y))
31 + 17y + 2y2 = ((5 * 5 + y * 5) + y(5 + y))
31 + 17y + 2y2 = ((25 + 5y) + y(5 + y))
31 + 17y + 2y2 = (25 + 5y + (5 * y + y * y))
31 + 17y + 2y2 = (25 + 5y + (5y + y2))

Combine like terms: 5y + 5y = 10y
31 + 17y + 2y2 = (25 + 10y + y2)

Solving
31 + 17y + 2y2 = 25 + 10y + y2

Solving for variable 'y'.

Reorder the terms:
31 + -25 + 17y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 31 + -25 = 6
6 + 17y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 17y + -10y = 7y
6 + 7y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
6 + 7y + 1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Reorder the terms:
6 + 7y + 1y2 = 25 + -25 + 10y + -10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
6 + 7y + 1y2 = 0 + 10y + -10y + y2 + -1y2
6 + 7y + 1y2 = 10y + -10y + y2 + -1y2

Combine like terms: 10y + -10y = 0
6 + 7y + 1y2 = 0 + y2 + -1y2
6 + 7y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + 7y + 1y2 = 0

Factor a trinomial.
(6 + y)(1 + y) = 0


Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-6, -1}

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