2y^2+14y+21=(y+4)(y+4)

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Solution for 2y^2+14y+21=(y+4)(y+4) equation: 


Simplifying
2y2 + 14y + 21 = (y + 4)(y + 4)

Reorder the terms:
21 + 14y + 2y2 = (y + 4)(y + 4)

Reorder the terms:
21 + 14y + 2y2 = (4 + y)(y + 4)

Reorder the terms:
21 + 14y + 2y2 = (4 + y)(4 + y)

Multiply (4 + y) * (4 + y)
21 + 14y + 2y2 = (4(4 + y) + y(4 + y))
21 + 14y + 2y2 = ((4 * 4 + y * 4) + y(4 + y))
21 + 14y + 2y2 = ((16 + 4y) + y(4 + y))
21 + 14y + 2y2 = (16 + 4y + (4 * y + y * y))
21 + 14y + 2y2 = (16 + 4y + (4y + y2))

Combine like terms: 4y + 4y = 8y
21 + 14y + 2y2 = (16 + 8y + y2)

Solving
21 + 14y + 2y2 = 16 + 8y + y2

Solving for variable 'y'.

Reorder the terms:
21 + -16 + 14y + -8y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 21 + -16 = 5
5 + 14y + -8y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 14y + -8y = 6y
5 + 6y + 2y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
5 + 6y + 1y2 = 16 + 8y + y2 + -16 + -8y + -1y2

Reorder the terms:
5 + 6y + 1y2 = 16 + -16 + 8y + -8y + y2 + -1y2

Combine like terms: 16 + -16 = 0
5 + 6y + 1y2 = 0 + 8y + -8y + y2 + -1y2
5 + 6y + 1y2 = 8y + -8y + y2 + -1y2

Combine like terms: 8y + -8y = 0
5 + 6y + 1y2 = 0 + y2 + -1y2
5 + 6y + 1y2 = y2 + -1y2

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

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


Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5

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 = {-5, -1}

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