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

Solution for (n+3)(4n-3)=0 equation:

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

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

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

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

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

Solving
-9 + 9n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(3 + -4n) = 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 '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

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

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

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-3, 0.75}