(n+5)(n-7)=28

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Solution for (n+5)(n-7)=28 equation:


Simplifying
(n + 5)(n + -7) = 28

Reorder the terms:
(5 + n)(n + -7) = 28

Reorder the terms:
(5 + n)(-7 + n) = 28

Multiply (5 + n) * (-7 + n)
(5(-7 + n) + n(-7 + n)) = 28
((-7 * 5 + n * 5) + n(-7 + n)) = 28
((-35 + 5n) + n(-7 + n)) = 28
(-35 + 5n + (-7 * n + n * n)) = 28
(-35 + 5n + (-7n + n2)) = 28

Combine like terms: 5n + -7n = -2n
(-35 + -2n + n2) = 28

Solving
-35 + -2n + n2 = 28

Solving for variable 'n'.

Reorder the terms:
-35 + -28 + -2n + n2 = 28 + -28

Combine like terms: -35 + -28 = -63
-63 + -2n + n2 = 28 + -28

Combine like terms: 28 + -28 = 0
-63 + -2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(9 + -1n) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9

Solution

n = {-7, 9}

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