Move 54 to the left side of the equation by subtracting it from both sides.
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=2⋅-54=-108 and whose sum is b=3.
Factor 3 out of 3w.
Rewrite 3 as -9 plus 12
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, 2w-9.
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
Add 9 to both sides of the equation.
Divide each term by 2 and simplify.
Divide each term in 2w=9 by 2.
Cancel the common factor of 2.
Cancel the common factor.
Divide w by 1.
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
Subtract 6 from both sides of the equation.
The final solution is all the values that make (2w-9)(w+6)=0 true.
The result can be shown in multiple forms.
Mixed Number Form:
Solve for w 2w^2+3w=54