(n-3)(n+10)=

Solution for (n-3)(n+10)= equation:

Simplifying
(n + -3)(n + 10) = 0

Reorder the terms:
(-3 + n)(n + 10) = 0

Reorder the terms:
(-3 + n)(10 + n) = 0

Multiply (-3 + n) * (10 + n)
(-3(10 + n) + n(10 + n)) = 0
((10 * -3 + n * -3) + n(10 + n)) = 0
((-30 + -3n) + n(10 + n)) = 0
(-30 + -3n + (10 * n + n * n)) = 0
(-30 + -3n + (10n + n2)) = 0

Combine like terms: -3n + 10n = 7n
(-30 + 7n + n2) = 0

Solving
-30 + 7n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-10 + -1n)(3 + -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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-10, 3}