(5n+6)(5n-3)=0

Solution for (5n+6)(5n-3)=0 equation:

Simplifying
(5n + 6)(5n + -3) = 0

Reorder the terms:
(6 + 5n)(5n + -3) = 0

Reorder the terms:
(6 + 5n)(-3 + 5n) = 0

Multiply (6 + 5n) * (-3 + 5n)
(6(-3 + 5n) + 5n * (-3 + 5n)) = 0
((-3 * 6 + 5n * 6) + 5n * (-3 + 5n)) = 0
((-18 + 30n) + 5n * (-3 + 5n)) = 0
(-18 + 30n + (-3 * 5n + 5n * 5n)) = 0
(-18 + 30n + (-15n + 25n2)) = 0

Combine like terms: 30n + -15n = 15n
(-18 + 15n + 25n2) = 0

Solving
-18 + 15n + 25n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -5n)(3 + -5n) = 0

Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve:

Simplifying
-6 + -5n = 0

Solving
-6 + -5n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5n = 0 + 6
-5n = 0 + 6

Combine like terms: 0 + 6 = 6
-5n = 6

Divide each side by '-5'.
n = -1.2

Simplifying
n = -1.2
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

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

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

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

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {-1.2, 0.6}