n(51-3n)=-702

Solution for n(51-3n)=-702 equation:

Simplifying
n(51 + -3n) = -702
(51 * n + -3n * n) = -702
(51n + -3n2) = -702

Solving
51n + -3n2 = -702

Solving for variable 'n'.

Reorder the terms:
702 + 51n + -3n2 = -702 + 702

Combine like terms: -702 + 702 = 0
702 + 51n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(234 + 17n + -1n2) = 0

Factor a trinomial.
3((26 + -1n)(9 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(26 + -1n)' equal to zero and attempt to solve:

Simplifying
26 + -1n = 0

Solving
26 + -1n = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1n = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1n = 0 + -26
-1n = 0 + -26

Combine like terms: 0 + -26 = -26
-1n = -26

Divide each side by '-1'.
n = 26

Simplifying
n = 26
Subproblem 2
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Solution
n = {26, -9}