# Solve for w 12w^2+19w-21=0 12w2+19w-21=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=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 and solve.
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 and solve.
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

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