6n^2-15n+6=-3

Solution for 6n^2-15n+6=-3 equation:

Simplifying
6n2 + -15n + 6 = -3

Reorder the terms:
6 + -15n + 6n2 = -3

Solving
6 + -15n + 6n2 = -3

Solving for variable 'n'.

Reorder the terms:
6 + 3 + -15n + 6n2 = -3 + 3

Combine like terms: 6 + 3 = 9
9 + -15n + 6n2 = -3 + 3

Combine like terms: -3 + 3 = 0
9 + -15n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -5n + 2n2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
n = {1, 1.5}