(y+6)(y+6)=81

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Solution for (y+6)(y+6)=81 equation:


Simplifying
(y + 6)(y + 6) = 81

Reorder the terms:
(6 + y)(y + 6) = 81

Reorder the terms:
(6 + y)(6 + y) = 81

Multiply (6 + y) * (6 + y)
(6(6 + y) + y(6 + y)) = 81
((6 * 6 + y * 6) + y(6 + y)) = 81
((36 + 6y) + y(6 + y)) = 81
(36 + 6y + (6 * y + y * y)) = 81
(36 + 6y + (6y + y2)) = 81

Combine like terms: 6y + 6y = 12y
(36 + 12y + y2) = 81

Solving
36 + 12y + y2 = 81

Solving for variable 'y'.

Reorder the terms:
36 + -81 + 12y + y2 = 81 + -81

Combine like terms: 36 + -81 = -45
-45 + 12y + y2 = 81 + -81

Combine like terms: 81 + -81 = 0
-45 + 12y + y2 = 0

Factor a trinomial.
(-15 + -1y)(3 + -1y) = 0

Subproblem 1

Set the factor '(-15 + -1y)' equal to zero and attempt to solve: Simplifying -15 + -1y = 0 Solving -15 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1y = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1y = 0 + 15 -1y = 0 + 15 Combine like terms: 0 + 15 = 15 -1y = 15 Divide each side by '-1'. y = -15 Simplifying y = -15

Subproblem 2

Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3

Solution

y = {-15, 3}

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