(n-4)(n+10)=-48

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Solution for (n-4)(n+10)=-48 equation:


Simplifying
(n + -4)(n + 10) = -48

Reorder the terms:
(-4 + n)(n + 10) = -48

Reorder the terms:
(-4 + n)(10 + n) = -48

Multiply (-4 + n) * (10 + n)
(-4(10 + n) + n(10 + n)) = -48
((10 * -4 + n * -4) + n(10 + n)) = -48
((-40 + -4n) + n(10 + n)) = -48
(-40 + -4n + (10 * n + n * n)) = -48
(-40 + -4n + (10n + n2)) = -48

Combine like terms: -4n + 10n = 6n
(-40 + 6n + n2) = -48

Solving
-40 + 6n + n2 = -48

Solving for variable 'n'.

Reorder the terms:
-40 + 48 + 6n + n2 = -48 + 48

Combine like terms: -40 + 48 = 8
8 + 6n + n2 = -48 + 48

Combine like terms: -48 + 48 = 0
8 + 6n + n2 = 0

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

Subproblem 1

Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4

Subproblem 2

Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2

Solution

n = {-4, -2}

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