28n^2-45=3n^2-60n

Solution for 28n^2-45=3n^2-60n equation:

Simplifying
28n2 + -45 = 3n2 + -60n

Reorder the terms:
-45 + 28n2 = 3n2 + -60n

Reorder the terms:
-45 + 28n2 = -60n + 3n2

Solving
-45 + 28n2 = -60n + 3n2

Solving for variable 'n'.

Reorder the terms:
-45 + 60n + 28n2 + -3n2 = -60n + 3n2 + 60n + -3n2

Combine like terms: 28n2 + -3n2 = 25n2
-45 + 60n + 25n2 = -60n + 3n2 + 60n + -3n2

Reorder the terms:
-45 + 60n + 25n2 = -60n + 60n + 3n2 + -3n2

Combine like terms: -60n + 60n = 0
-45 + 60n + 25n2 = 0 + 3n2 + -3n2
-45 + 60n + 25n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-45 + 60n + 25n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 12n + 5n2) = 0

Factor a trinomial.
5((-3 + -1n)(3 + -5n)) = 0

Ignore the factor 5.
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 + -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 = {-3, 0.6}