(n+3)(n-7)=-25

Solution for (n+3)(n-7)=-25 equation:

Simplifying
(n + 3)(n + -7) = -25

Reorder the terms:
(3 + n)(n + -7) = -25

Reorder the terms:
(3 + n)(-7 + n) = -25

Multiply (3 + n) * (-7 + n)
(3(-7 + n) + n(-7 + n)) = -25
((-7 * 3 + n * 3) + n(-7 + n)) = -25
((-21 + 3n) + n(-7 + n)) = -25
(-21 + 3n + (-7 * n + n * n)) = -25
(-21 + 3n + (-7n + n2)) = -25

Combine like terms: 3n + -7n = -4n
(-21 + -4n + n2) = -25

Solving
-21 + -4n + n2 = -25

Solving for variable 'n'.

Reorder the terms:
-21 + 25 + -4n + n2 = -25 + 25

Combine like terms: -21 + 25 = 4
4 + -4n + n2 = -25 + 25

Combine like terms: -25 + 25 = 0
4 + -4n + n2 = 0

Factor a trinomial.
(2 + -1n)(2 + -1n) = 0

Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {2, 2}