(3n+1)(n-2)=40

Solution for (3n+1)(n-2)=40 equation:

Simplifying
(3n + 1)(n + -2) = 40

Reorder the terms:
(1 + 3n)(n + -2) = 40

Reorder the terms:
(1 + 3n)(-2 + n) = 40

Multiply (1 + 3n) * (-2 + n)
(1(-2 + n) + 3n * (-2 + n)) = 40
((-2 * 1 + n * 1) + 3n * (-2 + n)) = 40
((-2 + 1n) + 3n * (-2 + n)) = 40
(-2 + 1n + (-2 * 3n + n * 3n)) = 40
(-2 + 1n + (-6n + 3n2)) = 40

Combine like terms: 1n + -6n = -5n
(-2 + -5n + 3n2) = 40

Solving
-2 + -5n + 3n2 = 40

Solving for variable 'n'.

Reorder the terms:
-2 + -40 + -5n + 3n2 = 40 + -40

Combine like terms: -2 + -40 = -42
-42 + -5n + 3n2 = 40 + -40

Combine like terms: 40 + -40 = 0
-42 + -5n + 3n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-3, 4.666666667}