(y+2)(y+2)=2y^2+3y+2

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Solution for (y+2)(y+2)=2y^2+3y+2 equation: 


Simplifying
(y + 2)(y + 2) = 2y2 + 3y + 2

Reorder the terms:
(2 + y)(y + 2) = 2y2 + 3y + 2

Reorder the terms:
(2 + y)(2 + y) = 2y2 + 3y + 2

Multiply (2 + y) * (2 + y)
(2(2 + y) + y(2 + y)) = 2y2 + 3y + 2
((2 * 2 + y * 2) + y(2 + y)) = 2y2 + 3y + 2
((4 + 2y) + y(2 + y)) = 2y2 + 3y + 2
(4 + 2y + (2 * y + y * y)) = 2y2 + 3y + 2
(4 + 2y + (2y + y2)) = 2y2 + 3y + 2

Combine like terms: 2y + 2y = 4y
(4 + 4y + y2) = 2y2 + 3y + 2

Reorder the terms:
4 + 4y + y2 = 2 + 3y + 2y2

Solving
4 + 4y + y2 = 2 + 3y + 2y2

Solving for variable 'y'.

Reorder the terms:
4 + -2 + 4y + -3y + y2 + -2y2 = 2 + 3y + 2y2 + -2 + -3y + -2y2

Combine like terms: 4 + -2 = 2
2 + 4y + -3y + y2 + -2y2 = 2 + 3y + 2y2 + -2 + -3y + -2y2

Combine like terms: 4y + -3y = 1y
2 + 1y + y2 + -2y2 = 2 + 3y + 2y2 + -2 + -3y + -2y2

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

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

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

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

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

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