(n-7)(n-5)=0

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Solution for (n-7)(n-5)=0 equation:


Simplifying
(n + -7)(n + -5) = 0

Reorder the terms:
(-7 + n)(n + -5) = 0

Reorder the terms:
(-7 + n)(-5 + n) = 0

Multiply (-7 + n) * (-5 + n)
(-7(-5 + n) + n(-5 + n)) = 0
((-5 * -7 + n * -7) + n(-5 + n)) = 0
((35 + -7n) + n(-5 + n)) = 0
(35 + -7n + (-5 * n + n * n)) = 0
(35 + -7n + (-5n + n2)) = 0

Combine like terms: -7n + -5n = -12n
(35 + -12n + n2) = 0

Solving
35 + -12n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -1n)(7 + -1n) = 0

Subproblem 1

Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5

Subproblem 2

Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7

Solution

n = {5, 7}

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