n(n-21)=-98

Solution for n(n-21)=-98 equation:

Simplifying
n(n + -21) = -98

Reorder the terms:
n(-21 + n) = -98
(-21 * n + n * n) = -98
(-21n + n2) = -98

Solving
-21n + n2 = -98

Solving for variable 'n'.

Reorder the terms:
98 + -21n + n2 = -98 + 98

Combine like terms: -98 + 98 = 0
98 + -21n + n2 = 0

Factor a trinomial.
(7 + -1n)(14 + -1n) = 0

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

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {7, 14}