(2n-6)(2n+3)=

Solution for (2n-6)(2n+3)= equation:

Simplifying
(2n + -6)(2n + 3) = 0

Reorder the terms:
(-6 + 2n)(2n + 3) = 0

Reorder the terms:
(-6 + 2n)(3 + 2n) = 0

Multiply (-6 + 2n) * (3 + 2n)
(-6(3 + 2n) + 2n * (3 + 2n)) = 0
((3 * -6 + 2n * -6) + 2n * (3 + 2n)) = 0
((-18 + -12n) + 2n * (3 + 2n)) = 0
(-18 + -12n + (3 * 2n + 2n * 2n)) = 0
(-18 + -12n + (6n + 4n2)) = 0

Combine like terms: -12n + 6n = -6n
(-18 + -6n + 4n2) = 0

Solving
-18 + -6n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -3n + 2n2) = 0

Factor a trinomial.
2((-3 + -2n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 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 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
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 = {-1.5, 3}