(n+8)(n-3)=-30

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Solution for (n+8)(n-3)=-30 equation:


Simplifying
(n + 8)(n + -3) = -30

Reorder the terms:
(8 + n)(n + -3) = -30

Reorder the terms:
(8 + n)(-3 + n) = -30

Multiply (8 + n) * (-3 + n)
(8(-3 + n) + n(-3 + n)) = -30
((-3 * 8 + n * 8) + n(-3 + n)) = -30
((-24 + 8n) + n(-3 + n)) = -30
(-24 + 8n + (-3 * n + n * n)) = -30
(-24 + 8n + (-3n + n2)) = -30

Combine like terms: 8n + -3n = 5n
(-24 + 5n + n2) = -30

Solving
-24 + 5n + n2 = -30

Solving for variable 'n'.

Reorder the terms:
-24 + 30 + 5n + n2 = -30 + 30

Combine like terms: -24 + 30 = 6
6 + 5n + n2 = -30 + 30

Combine like terms: -30 + 30 = 0
6 + 5n + n2 = 0

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

Subproblem 1

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

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 = {-3, -2}

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