3n2+6-11n=0

Reorder terms.

3n2-11n+6=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅6=18 and whose sum is b=-11.

Factor -11 out of -11n.

3n2-11n+6=0

Rewrite -11 as -2 plus -9

3n2+(-2-9)n+6=0

Apply the distributive property.

3n2-2n-9n+6=0

3n2-2n-9n+6=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3n2-2n)-9n+6=0

Factor out the greatest common factor (GCF) from each group.

n(3n-2)-3(3n-2)=0

n(3n-2)-3(3n-2)=0

Factor the polynomial by factoring out the greatest common factor, 3n-2.

(3n-2)(n-3)=0

(3n-2)(n-3)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

3n-2=0

n-3=0

Set the first factor equal to 0.

3n-2=0

Add 2 to both sides of the equation.

3n=2

Divide each term by 3 and simplify.

Divide each term in 3n=2 by 3.

3n3=23

Cancel the common factor of 3.

Cancel the common factor.

3n3=23

Divide n by 1.

n=23

n=23

n=23

n=23

Set the next factor equal to 0.

n-3=0

Add 3 to both sides of the equation.

n=3

n=3

The final solution is all the values that make (3n-2)(n-3)=0 true.

n=23,3

The result can be shown in multiple forms.

Exact Form:

n=23,3

Decimal Form:

n=0.6‾,3

Solve for n 3n^2+6-11n=0