(n-4)(n+1)=0

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Solution for (n-4)(n+1)=0 equation:


Simplifying
(n + -4)(n + 1) = 0

Reorder the terms:
(-4 + n)(n + 1) = 0

Reorder the terms:
(-4 + n)(1 + n) = 0

Multiply (-4 + n) * (1 + n)
(-4(1 + n) + n(1 + n)) = 0
((1 * -4 + n * -4) + n(1 + n)) = 0
((-4 + -4n) + n(1 + n)) = 0
(-4 + -4n + (1 * n + n * n)) = 0
(-4 + -4n + (1n + n2)) = 0

Combine like terms: -4n + 1n = -3n
(-4 + -3n + n2) = 0

Solving
-4 + -3n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1

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

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 = {-1, 4}

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