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

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.

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.

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