(n+-3)(3n+4)=

Solution for (n+-3)(3n+4)= equation:

Simplifying
(n + -3)(3n + 4) = 0

Reorder the terms:
(-3 + n)(3n + 4) = 0

Reorder the terms:
(-3 + n)(4 + 3n) = 0

Multiply (-3 + n) * (4 + 3n)
(-3(4 + 3n) + n(4 + 3n)) = 0
((4 * -3 + 3n * -3) + n(4 + 3n)) = 0
((-12 + -9n) + n(4 + 3n)) = 0
(-12 + -9n + (4 * n + 3n * n)) = 0
(-12 + -9n + (4n + 3n2)) = 0

Combine like terms: -9n + 4n = -5n
(-12 + -5n + 3n2) = 0

Solving
-12 + -5n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -3n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve:

Simplifying
-4 + -3n = 0

Solving
-4 + -3n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3n = 0 + 4
-3n = 0 + 4

Combine like terms: 0 + 4 = 4
-3n = 4

Divide each side by '-3'.
n = -1.333333333

Simplifying
n = -1.333333333
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 = {-1.333333333, 3}