5n^2+25n-27=3

Solution for 5n^2+25n-27=3 equation:

Simplifying
5n2 + 25n + -27 = 3

Reorder the terms:
-27 + 25n + 5n2 = 3

Solving
-27 + 25n + 5n2 = 3

Solving for variable 'n'.

Reorder the terms:
-27 + -3 + 25n + 5n2 = 3 + -3

Combine like terms: -27 + -3 = -30
-30 + 25n + 5n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-30 + 25n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 5n + n2) = 0

Factor a trinomial.
5((-6 + -1n)(1 + -1n)) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 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 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-6, 1}