# Solve for w 2w^2+3w=54

2w2+3w=54
Move 54 to the left side of the equation by subtracting it from both sides.
2w2+3w-54=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=2⋅-54=-108 and whose sum is b=3.
Factor 3 out of 3w.
2w2+3(w)-54=0
Rewrite 3 as -9 plus 12
2w2+(-9+12)w-54=0
Apply the distributive property.
2w2-9w+12w-54=0
2w2-9w+12w-54=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2w2-9w)+12w-54=0
Factor out the greatest common factor (GCF) from each group.
w(2w-9)+6(2w-9)=0
w(2w-9)+6(2w-9)=0
Factor the polynomial by factoring out the greatest common factor, 2w-9.
(2w-9)(w+6)=0
(2w-9)(w+6)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2w-9=0
w+6=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
2w-9=0
Add 9 to both sides of the equation.
2w=9
Divide each term by 2 and simplify.
Divide each term in 2w=9 by 2.
2w2=92
Cancel the common factor of 2.
Cancel the common factor.
2w2=92
Divide w by 1.
w=92
w=92
w=92
w=92
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
w+6=0
Subtract 6 from both sides of the equation.
w=-6
w=-6
The final solution is all the values that make (2w-9)(w+6)=0 true.
w=92,-6
The result can be shown in multiple forms.
Exact Form:
w=92,-6
Decimal Form:
w=4.5,-6
Mixed Number Form:
w=412,-6
Solve for w 2w^2+3w=54