(n-3)(7n+6)=0

Solution for (n-3)(7n+6)=0 equation:

Simplifying
(n + -3)(7n + 6) = 0

Reorder the terms:
(-3 + n)(7n + 6) = 0

Reorder the terms:
(-3 + n)(6 + 7n) = 0

Multiply (-3 + n) * (6 + 7n)
(-3(6 + 7n) + n(6 + 7n)) = 0
((6 * -3 + 7n * -3) + n(6 + 7n)) = 0
((-18 + -21n) + n(6 + 7n)) = 0
(-18 + -21n + (6 * n + 7n * n)) = 0
(-18 + -21n + (6n + 7n2)) = 0

Combine like terms: -21n + 6n = -15n
(-18 + -15n + 7n2) = 0

Solving
-18 + -15n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -7n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -7n)' equal to zero and attempt to solve:

Simplifying
-6 + -7n = 0

Solving
-6 + -7n = 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 + -7n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7n = 0 + 6
-7n = 0 + 6

Combine like terms: 0 + 6 = 6
-7n = 6

Divide each side by '-7'.
n = -0.8571428571

Simplifying
n = -0.8571428571
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 = {-0.8571428571, 3}