1160=n(2n+18)

Solution for 1160=n(2n+18) equation:

Simplifying
1160 = n(2n + 18)

Reorder the terms:
1160 = n(18 + 2n)
1160 = (18 * n + 2n * n)
1160 = (18n + 2n2)

Solving
1160 = 18n + 2n2

Solving for variable 'n'.

Reorder the terms:
1160 + -18n + -2n2 = 18n + -18n + 2n2 + -2n2

Combine like terms: 18n + -18n = 0
1160 + -18n + -2n2 = 0 + 2n2 + -2n2
1160 + -18n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
1160 + -18n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(580 + -9n + -1n2) = 0

Factor a trinomial.
2((20 + -1n)(29 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Subproblem 2
Set the factor '(29 + n)' equal to zero and attempt to solve:

Simplifying
29 + n = 0

Solving
29 + n = 0

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

Add '-29' to each side of the equation.
29 + -29 + n = 0 + -29

Combine like terms: 29 + -29 = 0
0 + n = 0 + -29
n = 0 + -29

Combine like terms: 0 + -29 = -29
n = -29

Simplifying
n = -29
Solution
n = {20, -29}