2y^2+5y+31=y^2+10y+25

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Solution for 2y^2+5y+31=y^2+10y+25 equation: 


Simplifying
2y2 + 5y + 31 = y2 + 10y + 25

Reorder the terms:
31 + 5y + 2y2 = y2 + 10y + 25

Reorder the terms:
31 + 5y + 2y2 = 25 + 10y + y2

Solving
31 + 5y + 2y2 = 25 + 10y + y2

Solving for variable 'y'.

Reorder the terms:
31 + -25 + 5y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 31 + -25 = 6
6 + 5y + -10y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 5y + -10y = -5y
6 + -5y + 2y2 + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
6 + -5y + 1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Reorder the terms:
6 + -5y + 1y2 = 25 + -25 + 10y + -10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
6 + -5y + 1y2 = 0 + 10y + -10y + y2 + -1y2
6 + -5y + 1y2 = 10y + -10y + y2 + -1y2

Combine like terms: 10y + -10y = 0
6 + -5y + 1y2 = 0 + y2 + -1y2
6 + -5y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -5y + 1y2 = 0

Factor a trinomial.
(2 + -1y)(3 + -1y) = 0


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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2

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 = {2, 3}

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