(y+4)(y+4)=(2y+5)(y+6)

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Solution for (y+4)(y+4)=(2y+5)(y+6) equation: 


Simplifying
(y + 4)(y + 4) = (2y + 5)(y + 6)

Reorder the terms:
(4 + y)(y + 4) = (2y + 5)(y + 6)

Reorder the terms:
(4 + y)(4 + y) = (2y + 5)(y + 6)

Multiply (4 + y) * (4 + y)
(4(4 + y) + y(4 + y)) = (2y + 5)(y + 6)
((4 * 4 + y * 4) + y(4 + y)) = (2y + 5)(y + 6)
((16 + 4y) + y(4 + y)) = (2y + 5)(y + 6)
(16 + 4y + (4 * y + y * y)) = (2y + 5)(y + 6)
(16 + 4y + (4y + y2)) = (2y + 5)(y + 6)

Combine like terms: 4y + 4y = 8y
(16 + 8y + y2) = (2y + 5)(y + 6)

Reorder the terms:
16 + 8y + y2 = (5 + 2y)(y + 6)

Reorder the terms:
16 + 8y + y2 = (5 + 2y)(6 + y)

Multiply (5 + 2y) * (6 + y)
16 + 8y + y2 = (5(6 + y) + 2y * (6 + y))
16 + 8y + y2 = ((6 * 5 + y * 5) + 2y * (6 + y))
16 + 8y + y2 = ((30 + 5y) + 2y * (6 + y))
16 + 8y + y2 = (30 + 5y + (6 * 2y + y * 2y))
16 + 8y + y2 = (30 + 5y + (12y + 2y2))

Combine like terms: 5y + 12y = 17y
16 + 8y + y2 = (30 + 17y + 2y2)

Solving
16 + 8y + y2 = 30 + 17y + 2y2

Solving for variable 'y'.

Reorder the terms:
16 + -30 + 8y + -17y + y2 + -2y2 = 30 + 17y + 2y2 + -30 + -17y + -2y2

Combine like terms: 16 + -30 = -14
-14 + 8y + -17y + y2 + -2y2 = 30 + 17y + 2y2 + -30 + -17y + -2y2

Combine like terms: 8y + -17y = -9y
-14 + -9y + y2 + -2y2 = 30 + 17y + 2y2 + -30 + -17y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-14 + -9y + -1y2 = 30 + 17y + 2y2 + -30 + -17y + -2y2

Reorder the terms:
-14 + -9y + -1y2 = 30 + -30 + 17y + -17y + 2y2 + -2y2

Combine like terms: 30 + -30 = 0
-14 + -9y + -1y2 = 0 + 17y + -17y + 2y2 + -2y2
-14 + -9y + -1y2 = 17y + -17y + 2y2 + -2y2

Combine like terms: 17y + -17y = 0
-14 + -9y + -1y2 = 0 + 2y2 + -2y2
-14 + -9y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-14 + -9y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 9y + y2) = 0

Factor a trinomial.
-1((7 + y)(2 + y)) = 0

Ignore the factor -1.

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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