9(y+11)=(y+11)(y+13)

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Solution for 9(y+11)=(y+11)(y+13) equation: 


Simplifying
9(y + 11) = (y + 11)(y + 13)

Reorder the terms:
9(11 + y) = (y + 11)(y + 13)
(11 * 9 + y * 9) = (y + 11)(y + 13)
(99 + 9y) = (y + 11)(y + 13)

Reorder the terms:
99 + 9y = (11 + y)(y + 13)

Reorder the terms:
99 + 9y = (11 + y)(13 + y)

Multiply (11 + y) * (13 + y)
99 + 9y = (11(13 + y) + y(13 + y))
99 + 9y = ((13 * 11 + y * 11) + y(13 + y))
99 + 9y = ((143 + 11y) + y(13 + y))
99 + 9y = (143 + 11y + (13 * y + y * y))
99 + 9y = (143 + 11y + (13y + y2))

Combine like terms: 11y + 13y = 24y
99 + 9y = (143 + 24y + y2)

Solving
99 + 9y = 143 + 24y + y2

Solving for variable 'y'.

Reorder the terms:
99 + -143 + 9y + -24y + -1y2 = 143 + 24y + y2 + -143 + -24y + -1y2

Combine like terms: 99 + -143 = -44
-44 + 9y + -24y + -1y2 = 143 + 24y + y2 + -143 + -24y + -1y2

Combine like terms: 9y + -24y = -15y
-44 + -15y + -1y2 = 143 + 24y + y2 + -143 + -24y + -1y2

Reorder the terms:
-44 + -15y + -1y2 = 143 + -143 + 24y + -24y + y2 + -1y2

Combine like terms: 143 + -143 = 0
-44 + -15y + -1y2 = 0 + 24y + -24y + y2 + -1y2
-44 + -15y + -1y2 = 24y + -24y + y2 + -1y2

Combine like terms: 24y + -24y = 0
-44 + -15y + -1y2 = 0 + y2 + -1y2
-44 + -15y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-44 + -15y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(44 + 15y + y2) = 0

Factor a trinomial.
-1((11 + y)(4 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

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

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {-11, -4}

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