2y^2+21y+50=(y+6)(y+6)

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Solution for 2y^2+21y+50=(y+6)(y+6) equation: 


Simplifying
2y2 + 21y + 50 = (y + 6)(y + 6)

Reorder the terms:
50 + 21y + 2y2 = (y + 6)(y + 6)

Reorder the terms:
50 + 21y + 2y2 = (6 + y)(y + 6)

Reorder the terms:
50 + 21y + 2y2 = (6 + y)(6 + y)

Multiply (6 + y) * (6 + y)
50 + 21y + 2y2 = (6(6 + y) + y(6 + y))
50 + 21y + 2y2 = ((6 * 6 + y * 6) + y(6 + y))
50 + 21y + 2y2 = ((36 + 6y) + y(6 + y))
50 + 21y + 2y2 = (36 + 6y + (6 * y + y * y))
50 + 21y + 2y2 = (36 + 6y + (6y + y2))

Combine like terms: 6y + 6y = 12y
50 + 21y + 2y2 = (36 + 12y + y2)

Solving
50 + 21y + 2y2 = 36 + 12y + y2

Solving for variable 'y'.

Reorder the terms:
50 + -36 + 21y + -12y + 2y2 + -1y2 = 36 + 12y + y2 + -36 + -12y + -1y2

Combine like terms: 50 + -36 = 14
14 + 21y + -12y + 2y2 + -1y2 = 36 + 12y + y2 + -36 + -12y + -1y2

Combine like terms: 21y + -12y = 9y
14 + 9y + 2y2 + -1y2 = 36 + 12y + y2 + -36 + -12y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
14 + 9y + 1y2 = 36 + 12y + y2 + -36 + -12y + -1y2

Reorder the terms:
14 + 9y + 1y2 = 36 + -36 + 12y + -12y + y2 + -1y2

Combine like terms: 36 + -36 = 0
14 + 9y + 1y2 = 0 + 12y + -12y + y2 + -1y2
14 + 9y + 1y2 = 12y + -12y + y2 + -1y2

Combine like terms: 12y + -12y = 0
14 + 9y + 1y2 = 0 + y2 + -1y2
14 + 9y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
14 + 9y + 1y2 = 0

Factor a trinomial.
(7 + y)(2 + y) = 0


Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

Subproblem 2
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
Solution
y = {-7, -2}

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