(n+7)(n-2)=36

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Solution for (n+7)(n-2)=36 equation:


Simplifying
(n + 7)(n + -2) = 36

Reorder the terms:
(7 + n)(n + -2) = 36

Reorder the terms:
(7 + n)(-2 + n) = 36

Multiply (7 + n) * (-2 + n)
(7(-2 + n) + n(-2 + n)) = 36
((-2 * 7 + n * 7) + n(-2 + n)) = 36
((-14 + 7n) + n(-2 + n)) = 36
(-14 + 7n + (-2 * n + n * n)) = 36
(-14 + 7n + (-2n + n2)) = 36

Combine like terms: 7n + -2n = 5n
(-14 + 5n + n2) = 36

Solving
-14 + 5n + n2 = 36

Solving for variable 'n'.

Reorder the terms:
-14 + -36 + 5n + n2 = 36 + -36

Combine like terms: -14 + -36 = -50
-50 + 5n + n2 = 36 + -36

Combine like terms: 36 + -36 = 0
-50 + 5n + n2 = 0

Factor a trinomial.
(-10 + -1n)(5 + -1n) = 0


Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10

Subproblem 2
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
Solution
n = {-10, 5}

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