(2n+5)(n-4)=15

Solution for (2n+5)(n-4)=15 equation:

Simplifying
(2n + 5)(n + -4) = 15

Reorder the terms:
(5 + 2n)(n + -4) = 15

Reorder the terms:
(5 + 2n)(-4 + n) = 15

Multiply (5 + 2n) * (-4 + n)
(5(-4 + n) + 2n * (-4 + n)) = 15
((-4 * 5 + n * 5) + 2n * (-4 + n)) = 15
((-20 + 5n) + 2n * (-4 + n)) = 15
(-20 + 5n + (-4 * 2n + n * 2n)) = 15
(-20 + 5n + (-8n + 2n2)) = 15

Combine like terms: 5n + -8n = -3n
(-20 + -3n + 2n2) = 15

Solving
-20 + -3n + 2n2 = 15

Solving for variable 'n'.

Reorder the terms:
-20 + -15 + -3n + 2n2 = 15 + -15

Combine like terms: -20 + -15 = -35
-35 + -3n + 2n2 = 15 + -15

Combine like terms: 15 + -15 = 0
-35 + -3n + 2n2 = 0

Factor a trinomial.
(-7 + -2n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve:

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 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 + -2n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5
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 = {-3.5, 5}