12w2+19w-21=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=12⋅-21=-252 and whose sum is b=19.

Factor 19 out of 19w.

12w2+19(w)-21=0

Rewrite 19 as -9 plus 28

12w2+(-9+28)w-21=0

Apply the distributive property.

12w2-9w+28w-21=0

12w2-9w+28w-21=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(12w2-9w)+28w-21=0

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

3w(4w-3)+7(4w-3)=0

3w(4w-3)+7(4w-3)=0

Factor the polynomial by factoring out the greatest common factor, 4w-3.

(4w-3)(3w+7)=0

(4w-3)(3w+7)=0

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

4w-3=0

3w+7=0

Set the first factor equal to 0.

4w-3=0

Add 3 to both sides of the equation.

4w=3

Divide each term by 4 and simplify.

Divide each term in 4w=3 by 4.

4w4=34

Cancel the common factor of 4.

Cancel the common factor.

4w4=34

Divide w by 1.

w=34

w=34

w=34

w=34

Set the next factor equal to 0.

3w+7=0

Subtract 7 from both sides of the equation.

3w=-7

Divide each term by 3 and simplify.

Divide each term in 3w=-7 by 3.

3w3=-73

Cancel the common factor of 3.

Cancel the common factor.

3w3=-73

Divide w by 1.

w=-73

w=-73

Move the negative in front of the fraction.

w=-73

w=-73

w=-73

The final solution is all the values that make (4w-3)(3w+7)=0 true.

w=34,-73

The result can be shown in multiple forms.

Exact Form:

w=34,-73

Decimal Form:

w=0.75,-2.3‾

Mixed Number Form:

w=34,-213

Solve for w 12w^2+19w-21=0