3u2-6=7u

Subtract 7u from both sides of the equation.

3u2-6-7u=0

Reorder terms.

3u2-7u-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=-7.

Factor -7 out of -7u.

3u2-7u-6=0

Rewrite -7 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

Subtract 2 from 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

Move the negative in front of the fraction.

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^2-6=7u