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

3n2+6-11n=0
Factor by grouping.
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 and solve.
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 and solve.
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

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