2y^2+6y+56=(y+7)(y+7)

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Solution for 2y^2+6y+56=(y+7)(y+7) equation: 


Simplifying
2y2 + 6y + 56 = (y + 7)(y + 7)

Reorder the terms:
56 + 6y + 2y2 = (y + 7)(y + 7)

Reorder the terms:
56 + 6y + 2y2 = (7 + y)(y + 7)

Reorder the terms:
56 + 6y + 2y2 = (7 + y)(7 + y)

Multiply (7 + y) * (7 + y)
56 + 6y + 2y2 = (7(7 + y) + y(7 + y))
56 + 6y + 2y2 = ((7 * 7 + y * 7) + y(7 + y))
56 + 6y + 2y2 = ((49 + 7y) + y(7 + y))
56 + 6y + 2y2 = (49 + 7y + (7 * y + y * y))
56 + 6y + 2y2 = (49 + 7y + (7y + y2))

Combine like terms: 7y + 7y = 14y
56 + 6y + 2y2 = (49 + 14y + y2)

Solving
56 + 6y + 2y2 = 49 + 14y + y2

Solving for variable 'y'.

Reorder the terms:
56 + -49 + 6y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 56 + -49 = 7
7 + 6y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 6y + -14y = -8y
7 + -8y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
7 + -8y + 1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Reorder the terms:
7 + -8y + 1y2 = 49 + -49 + 14y + -14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
7 + -8y + 1y2 = 0 + 14y + -14y + y2 + -1y2
7 + -8y + 1y2 = 14y + -14y + y2 + -1y2

Combine like terms: 14y + -14y = 0
7 + -8y + 1y2 = 0 + y2 + -1y2
7 + -8y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
7 + -8y + 1y2 = 0

Factor a trinomial.
(1 + -1y)(7 + -1y) = 0


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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

Divide each side by '-1'.
y = 1

Simplifying
y = 1

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {1, 7}

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