# Solve for u 3u^2=11u-6 3u2=11u-6
Subtract 11u from both sides of the equation.
3u2-11u=-6
Move 6 to the left side of the equation by adding it to both sides.
3u2-11u+6=0
Factor by grouping.
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 -11u.
3u2-11u+6=0
Rewrite -11 as -2 plus -9
3u2+(-2-9)u+6=0
Apply the distributive property.
3u2-2u-9u+6=0
3u2-2u-9u+6=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3u2-2u)-9u+6=0
Factor out the greatest common factor (GCF) from each group.
u(3u-2)-3(3u-2)=0
u(3u-2)-3(3u-2)=0
Factor the polynomial by factoring out the greatest common factor, 3u-2.
(3u-2)(u-3)=0
(3u-2)(u-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.
3u-2=0
u-3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3u-2=0
Add 2 to both sides of the equation.
3u=2
Divide each term by 3 and simplify.
Divide each term in 3u=2 by 3.
3u3=23
Cancel the common factor of 3.
Cancel the common factor.
3u3=23
Divide u by 1.
u=23
u=23
u=23
u=23
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
u-3=0
Add 3 to both sides of the equation.
u=3
u=3
The final solution is all the values that make (3u-2)(u-3)=0 true.
u=23,3
The result can be shown in multiple forms.
Exact Form:
u=23,3
Decimal Form:
u=0.6‾,3
Solve for u 3u^2=11u-6

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