(2n+5)(2n-5)=15n

Solution for (2n+5)(2n-5)=15n equation:

Simplifying
(2n + 5)(2n + -5) = 15n

Reorder the terms:
(5 + 2n)(2n + -5) = 15n

Reorder the terms:
(5 + 2n)(-5 + 2n) = 15n

Multiply (5 + 2n) * (-5 + 2n)
(5(-5 + 2n) + 2n * (-5 + 2n)) = 15n
((-5 * 5 + 2n * 5) + 2n * (-5 + 2n)) = 15n
((-25 + 10n) + 2n * (-5 + 2n)) = 15n
(-25 + 10n + (-5 * 2n + 2n * 2n)) = 15n
(-25 + 10n + (-10n + 4n2)) = 15n

Combine like terms: 10n + -10n = 0
(-25 + 0 + 4n2) = 15n
(-25 + 4n2) = 15n

Solving
-25 + 4n2 = 15n

Solving for variable 'n'.

Reorder the terms:
-25 + -15n + 4n2 = 15n + -15n

Combine like terms: 15n + -15n = 0
-25 + -15n + 4n2 = 0

Factor a trinomial.
(-5 + -4n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -4n)' equal to zero and attempt to solve:

Simplifying
-5 + -4n = 0

Solving
-5 + -4n = 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 + -4n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4n = 0 + 5
-4n = 0 + 5

Combine like terms: 0 + 5 = 5
-4n = 5

Divide each side by '-4'.
n = -1.25

Simplifying
n = -1.25
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 = {-1.25, 5}