=(n+2)(2n+5)

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

Simplifying
0 = (n + 2)(2n + 5)

Reorder the terms:
0 = (2 + n)(2n + 5)

Reorder the terms:
0 = (2 + n)(5 + 2n)

Multiply (2 + n) * (5 + 2n)
0 = (2(5 + 2n) + n(5 + 2n))
0 = ((5 * 2 + 2n * 2) + n(5 + 2n))
0 = ((10 + 4n) + n(5 + 2n))
0 = (10 + 4n + (5 * n + 2n * n))
0 = (10 + 4n + (5n + 2n2))

Combine like terms: 4n + 5n = 9n
0 = (10 + 9n + 2n2)

Solving
0 = 10 + 9n + 2n2

Solving for variable 'n'.

Combine like terms: 0 + -10 = -10
-10 + -9n + -2n2 = 10 + 9n + 2n2 + -10 + -9n + -2n2

Reorder the terms:
-10 + -9n + -2n2 = 10 + -10 + 9n + -9n + 2n2 + -2n2

Combine like terms: 10 + -10 = 0
-10 + -9n + -2n2 = 0 + 9n + -9n + 2n2 + -2n2
-10 + -9n + -2n2 = 9n + -9n + 2n2 + -2n2

Combine like terms: 9n + -9n = 0
-10 + -9n + -2n2 = 0 + 2n2 + -2n2
-10 + -9n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-10 + -9n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 9n + 2n2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 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 + 2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2n = 0 + -5
2n = 0 + -5

Combine like terms: 0 + -5 = -5
2n = -5

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Solution
n = {-2.5, -2}