(y+6)(y+6)=1

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Solution for (y+6)(y+6)=1 equation:


Simplifying
(y + 6)(y + 6) = 1

Reorder the terms:
(6 + y)(y + 6) = 1

Reorder the terms:
(6 + y)(6 + y) = 1

Multiply (6 + y) * (6 + y)
(6(6 + y) + y(6 + y)) = 1
((6 * 6 + y * 6) + y(6 + y)) = 1
((36 + 6y) + y(6 + y)) = 1
(36 + 6y + (6 * y + y * y)) = 1
(36 + 6y + (6y + y2)) = 1

Combine like terms: 6y + 6y = 12y
(36 + 12y + y2) = 1

Solving
36 + 12y + y2 = 1

Solving for variable 'y'.

Reorder the terms:
36 + -1 + 12y + y2 = 1 + -1

Combine like terms: 36 + -1 = 35
35 + 12y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
35 + 12y + y2 = 0

Factor a trinomial.
(7 + y)(5 + y) = 0

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 '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Solution

y = {-7, -5}

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