2w2+3w=54

Move 54 to the left side of the equation by subtracting it from both sides.

2w2+3w-54=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=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.

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.

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