n*(n-3)=180

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Solution for n*(n-3)=180 equation:


Simplifying
n(n + -3) = 180

Reorder the terms:
n(-3 + n) = 180
(-3 * n + n * n) = 180
(-3n + n2) = 180

Solving
-3n + n2 = 180

Solving for variable 'n'.

Reorder the terms:
-180 + -3n + n2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -3n + n2 = 0

Factor a trinomial.
(-12 + -1n)(15 + -1n) = 0

Subproblem 1

Set the factor '(-12 + -1n)' equal to zero and attempt to solve: Simplifying -12 + -1n = 0 Solving -12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1n = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1n = 0 + 12 -1n = 0 + 12 Combine like terms: 0 + 12 = 12 -1n = 12 Divide each side by '-1'. n = -12 Simplifying n = -12

Subproblem 2

Set the factor '(15 + -1n)' equal to zero and attempt to solve: Simplifying 15 + -1n = 0 Solving 15 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1n = 0 + -15 -1n = 0 + -15 Combine like terms: 0 + -15 = -15 -1n = -15 Divide each side by '-1'. n = 15 Simplifying n = 15

Solution

n = {-12, 15}

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