y^2+2y+1=2y^2+5y+3

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Solution for y^2+2y+1=2y^2+5y+3 equation: 


Simplifying
y2 + 2y + 1 = 2y2 + 5y + 3

Reorder the terms:
1 + 2y + y2 = 2y2 + 5y + 3

Reorder the terms:
1 + 2y + y2 = 3 + 5y + 2y2

Solving
1 + 2y + y2 = 3 + 5y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + -3 + 2y + -5y + y2 + -2y2 = 3 + 5y + 2y2 + -3 + -5y + -2y2

Combine like terms: 1 + -3 = -2
-2 + 2y + -5y + y2 + -2y2 = 3 + 5y + 2y2 + -3 + -5y + -2y2

Combine like terms: 2y + -5y = -3y
-2 + -3y + y2 + -2y2 = 3 + 5y + 2y2 + -3 + -5y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-2 + -3y + -1y2 = 3 + 5y + 2y2 + -3 + -5y + -2y2

Reorder the terms:
-2 + -3y + -1y2 = 3 + -3 + 5y + -5y + 2y2 + -2y2

Combine like terms: 3 + -3 = 0
-2 + -3y + -1y2 = 0 + 5y + -5y + 2y2 + -2y2
-2 + -3y + -1y2 = 5y + -5y + 2y2 + -2y2

Combine like terms: 5y + -5y = 0
-2 + -3y + -1y2 = 0 + 2y2 + -2y2
-2 + -3y + -1y2 = 2y2 + -2y2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 3y + y2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

Simplifying
y = -2

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 = {-2, -1}

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