(n-6)(n+6)=n-6

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Solution for (n-6)(n+6)=n-6 equation:


Simplifying
(n + -6)(n + 6) = n + -6

Reorder the terms:
(-6 + n)(n + 6) = n + -6

Reorder the terms:
(-6 + n)(6 + n) = n + -6

Multiply (-6 + n) * (6 + n)
(-6(6 + n) + n(6 + n)) = n + -6
((6 * -6 + n * -6) + n(6 + n)) = n + -6
((-36 + -6n) + n(6 + n)) = n + -6
(-36 + -6n + (6 * n + n * n)) = n + -6
(-36 + -6n + (6n + n2)) = n + -6

Combine like terms: -6n + 6n = 0
(-36 + 0 + n2) = n + -6
(-36 + n2) = n + -6

Reorder the terms:
-36 + n2 = -6 + n

Solving
-36 + n2 = -6 + n

Solving for variable 'n'.

Reorder the terms:
-36 + 6 + -1n + n2 = -6 + n + 6 + -1n

Combine like terms: -36 + 6 = -30
-30 + -1n + n2 = -6 + n + 6 + -1n

Reorder the terms:
-30 + -1n + n2 = -6 + 6 + n + -1n

Combine like terms: -6 + 6 = 0
-30 + -1n + n2 = 0 + n + -1n
-30 + -1n + n2 = n + -1n

Combine like terms: n + -1n = 0
-30 + -1n + n2 = 0

Factor a trinomial.
(-5 + -1n)(6 + -1n) = 0

Subproblem 1

Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5

Subproblem 2

Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6

Solution

n = {-5, 6}

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