(n-10)(n+7)=0

Solution for (n-10)(n+7)=0 equation:

Simplifying
(n + -10)(n + 7) = 0

Reorder the terms:
(-10 + n)(n + 7) = 0

Reorder the terms:
(-10 + n)(7 + n) = 0

Multiply (-10 + n) * (7 + n)
(-10(7 + n) + n(7 + n)) = 0
((7 * -10 + n * -10) + n(7 + n)) = 0
((-70 + -10n) + n(7 + n)) = 0
(-70 + -10n + (7 * n + n * n)) = 0
(-70 + -10n + (7n + n2)) = 0

Combine like terms: -10n + 7n = -3n
(-70 + -3n + n2) = 0

Solving
-70 + -3n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -1n)(10 + -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 '(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
Solution
n = {-7, 10}