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

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

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

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

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

Multiply (-4 + 3n) * (3 + 4n)
(-4(3 + 4n) + 3n * (3 + 4n)) = 0
((3 * -4 + 4n * -4) + 3n * (3 + 4n)) = 0
((-12 + -16n) + 3n * (3 + 4n)) = 0
(-12 + -16n + (3 * 3n + 4n * 3n)) = 0
(-12 + -16n + (9n + 12n2)) = 0

Combine like terms: -16n + 9n = -7n
(-12 + -7n + 12n2) = 0

Solving
-12 + -7n + 12n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-0.75, 1.333333333}