2y^2+5y+3=(y+3)(y+3)

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Solution for 2y^2+5y+3=(y+3)(y+3) equation: 


Simplifying
2y2 + 5y + 3 = (y + 3)(y + 3)

Reorder the terms:
3 + 5y + 2y2 = (y + 3)(y + 3)

Reorder the terms:
3 + 5y + 2y2 = (3 + y)(y + 3)

Reorder the terms:
3 + 5y + 2y2 = (3 + y)(3 + y)

Multiply (3 + y) * (3 + y)
3 + 5y + 2y2 = (3(3 + y) + y(3 + y))
3 + 5y + 2y2 = ((3 * 3 + y * 3) + y(3 + y))
3 + 5y + 2y2 = ((9 + 3y) + y(3 + y))
3 + 5y + 2y2 = (9 + 3y + (3 * y + y * y))
3 + 5y + 2y2 = (9 + 3y + (3y + y2))

Combine like terms: 3y + 3y = 6y
3 + 5y + 2y2 = (9 + 6y + y2)

Solving
3 + 5y + 2y2 = 9 + 6y + y2

Solving for variable 'y'.

Reorder the terms:
3 + -9 + 5y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 3 + -9 = -6
-6 + 5y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 5y + -6y = -1y
-6 + -1y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-6 + -1y + 1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Reorder the terms:
-6 + -1y + 1y2 = 9 + -9 + 6y + -6y + y2 + -1y2

Combine like terms: 9 + -9 = 0
-6 + -1y + 1y2 = 0 + 6y + -6y + y2 + -1y2
-6 + -1y + 1y2 = 6y + -6y + y2 + -1y2

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

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