(w-4)2+4w2-w=18

Move 18 to the left side of the equation by subtracting it from both sides.

(w-4)2+4w2-w-18=0

Rewrite (w-4)2 as (w-4)(w-4).

(w-4)(w-4)+4w2-w-18=0

Expand (w-4)(w-4) using the FOIL Method.

Apply the distributive property.

w(w-4)-4(w-4)+4w2-w-18=0

Apply the distributive property.

w⋅w+w⋅-4-4(w-4)+4w2-w-18=0

Apply the distributive property.

w⋅w+w⋅-4-4w-4⋅-4+4w2-w-18=0

w⋅w+w⋅-4-4w-4⋅-4+4w2-w-18=0

Simplify and combine like terms.

Simplify each term.

Multiply w by w.

w2+w⋅-4-4w-4⋅-4+4w2-w-18=0

Move -4 to the left of w.

w2-4w-4w-4⋅-4+4w2-w-18=0

Multiply -4 by -4.

w2-4w-4w+16+4w2-w-18=0

w2-4w-4w+16+4w2-w-18=0

Subtract 4w from -4w.

w2-8w+16+4w2-w-18=0

w2-8w+16+4w2-w-18=0

Add w2 and 4w2.

5w2-8w+16-w-18=0

Subtract w from -8w.

5w2-9w+16-18=0

Subtract 18 from 16.

5w2-9w-2=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=5⋅-2=-10 and whose sum is b=-9.

Factor -9 out of -9w.

5w2-9w-2=0

Rewrite -9 as 1 plus -10

5w2+(1-10)w-2=0

Apply the distributive property.

5w2+1w-10w-2=0

Multiply w by 1.

5w2+w-10w-2=0

5w2+w-10w-2=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(5w2+w)-10w-2=0

Factor out the greatest common factor (GCF) from each group.

w(5w+1)-2(5w+1)=0

w(5w+1)-2(5w+1)=0

Factor the polynomial by factoring out the greatest common factor, 5w+1.

(5w+1)(w-2)=0

(5w+1)(w-2)=0

(5w+1)(w-2)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

5w+1=0

w-2=0

Set the first factor equal to 0.

5w+1=0

Subtract 1 from both sides of the equation.

5w=-1

Divide each term by 5 and simplify.

Divide each term in 5w=-1 by 5.

5w5=-15

Cancel the common factor of 5.

Cancel the common factor.

5w5=-15

Divide w by 1.

w=-15

w=-15

Move the negative in front of the fraction.

w=-15

w=-15

w=-15

Set the next factor equal to 0.

w-2=0

Add 2 to both sides of the equation.

w=2

w=2

The final solution is all the values that make (5w+1)(w-2)=0 true.

w=-15,2

The result can be shown in multiple forms.

Exact Form:

w=-15,2

Decimal Form:

w=-0.2,2

Solve for w (w-4)^2+4w^2-w=18