3n^2=-5n+42

Solution for 3n^2=-5n+42 equation:

Simplifying
3n2 = -5n + 42

Reorder the terms:
3n2 = 42 + -5n

Solving
3n2 = 42 + -5n

Solving for variable 'n'.

Reorder the terms:
-42 + 5n + 3n2 = 42 + -5n + -42 + 5n

Reorder the terms:
-42 + 5n + 3n2 = 42 + -42 + -5n + 5n

Combine like terms: 42 + -42 = 0
-42 + 5n + 3n2 = 0 + -5n + 5n
-42 + 5n + 3n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
-42 + 5n + 3n2 = 0

Factor a trinomial.
(-14 + -3n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-14 + -3n)' equal to zero and attempt to solve:

Simplifying
-14 + -3n = 0

Solving
-14 + -3n = 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 + -3n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3n = 0 + 14
-3n = 0 + 14

Combine like terms: 0 + 14 = 14
-3n = 14

Divide each side by '-3'.
n = -4.666666667

Simplifying
n = -4.666666667
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4.666666667, 3}