(2y+9)(2y+9)=81

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Solution for (2y+9)(2y+9)=81 equation: 


Simplifying
(2y + 9)(2y + 9) = 81

Reorder the terms:
(9 + 2y)(2y + 9) = 81

Reorder the terms:
(9 + 2y)(9 + 2y) = 81

Multiply (9 + 2y) * (9 + 2y)
(9(9 + 2y) + 2y * (9 + 2y)) = 81
((9 * 9 + 2y * 9) + 2y * (9 + 2y)) = 81
((81 + 18y) + 2y * (9 + 2y)) = 81
(81 + 18y + (9 * 2y + 2y * 2y)) = 81
(81 + 18y + (18y + 4y2)) = 81

Combine like terms: 18y + 18y = 36y
(81 + 36y + 4y2) = 81

Add '-81' to each side of the equation.
81 + 36y + -81 + 4y2 = 81 + -81

Reorder the terms:
81 + -81 + 36y + 4y2 = 81 + -81

Combine like terms: 81 + -81 = 0
0 + 36y + 4y2 = 81 + -81
36y + 4y2 = 81 + -81

Combine like terms: 81 + -81 = 0
36y + 4y2 = 0

Solving
36y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(9 + y) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
Solution
y = {0, -9}

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