# Solve for u 3u^2-6=7u 3u2-6=7u
Subtract 7u from both sides of the equation.
3u2-6-7u=0
Factor by grouping.
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 and solve.
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 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^2-6=7u

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