5n^2+15n-46=4

Solution for 5n^2+15n-46=4 equation:

Simplifying
5n2 + 15n + -46 = 4

Reorder the terms:
-46 + 15n + 5n2 = 4

Solving
-46 + 15n + 5n2 = 4

Solving for variable 'n'.

Reorder the terms:
-46 + -4 + 15n + 5n2 = 4 + -4

Combine like terms: -46 + -4 = -50
-50 + 15n + 5n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-50 + 15n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + 3n + n2) = 0

Factor a trinomial.
5((-5 + -1n)(2 + -1n)) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-5, 2}