(n-4)(n+2)=0

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Solution for (n-4)(n+2)=0 equation:


Simplifying
(n + -4)(n + 2) = 0

Reorder the terms:
(-4 + n)(n + 2) = 0

Reorder the terms:
(-4 + n)(2 + n) = 0

Multiply (-4 + n) * (2 + n)
(-4(2 + n) + n(2 + n)) = 0
((2 * -4 + n * -4) + n(2 + n)) = 0
((-8 + -4n) + n(2 + n)) = 0
(-8 + -4n + (2 * n + n * n)) = 0
(-8 + -4n + (2n + n2)) = 0

Combine like terms: -4n + 2n = -2n
(-8 + -2n + n2) = 0

Solving
-8 + -2n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -1n)(4 + -1n) = 0

Subproblem 1

Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2

Subproblem 2

Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4

Solution

n = {-2, 4}

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