2y^2+9y+43=(y+7)(y+7)

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Solution for 2y^2+9y+43=(y+7)(y+7) equation: 


Simplifying
2y2 + 9y + 43 = (y + 7)(y + 7)

Reorder the terms:
43 + 9y + 2y2 = (y + 7)(y + 7)

Reorder the terms:
43 + 9y + 2y2 = (7 + y)(y + 7)

Reorder the terms:
43 + 9y + 2y2 = (7 + y)(7 + y)

Multiply (7 + y) * (7 + y)
43 + 9y + 2y2 = (7(7 + y) + y(7 + y))
43 + 9y + 2y2 = ((7 * 7 + y * 7) + y(7 + y))
43 + 9y + 2y2 = ((49 + 7y) + y(7 + y))
43 + 9y + 2y2 = (49 + 7y + (7 * y + y * y))
43 + 9y + 2y2 = (49 + 7y + (7y + y2))

Combine like terms: 7y + 7y = 14y
43 + 9y + 2y2 = (49 + 14y + y2)

Solving
43 + 9y + 2y2 = 49 + 14y + y2

Solving for variable 'y'.

Reorder the terms:
43 + -49 + 9y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 43 + -49 = -6
-6 + 9y + -14y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 9y + -14y = -5y
-6 + -5y + 2y2 + -1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-6 + -5y + 1y2 = 49 + 14y + y2 + -49 + -14y + -1y2

Reorder the terms:
-6 + -5y + 1y2 = 49 + -49 + 14y + -14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
-6 + -5y + 1y2 = 0 + 14y + -14y + y2 + -1y2
-6 + -5y + 1y2 = 14y + -14y + y2 + -1y2

Combine like terms: 14y + -14y = 0
-6 + -5y + 1y2 = 0 + y2 + -1y2
-6 + -5y + 1y2 = y2 + -1y2

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

Factor a trinomial.
(-1 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

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

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

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-1, 6}

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