Solve for v 2v^2+v-36=0

2v2+v-36=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⋅-36=-72 and whose sum is b=1.
Multiply by 1.
2v2+1v-36=0
Rewrite 1 as -8 plus 9
2v2+(-8+9)v-36=0
Apply the distributive property.
2v2-8v+9v-36=0
2v2-8v+9v-36=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2v2-8v)+9v-36=0
Factor out the greatest common factor (GCF) from each group.
2v(v-4)+9(v-4)=0
2v(v-4)+9(v-4)=0
Factor the polynomial by factoring out the greatest common factor, v-4.
(v-4)(2v+9)=0
(v-4)(2v+9)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
v-4=0
2v+9=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
v-4=0
Add 4 to both sides of the equation.
v=4
v=4
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
2v+9=0
Subtract 9 from both sides of the equation.
2v=-9
Divide each term by 2 and simplify.
Divide each term in 2v=-9 by 2.
2v2=-92
Cancel the common factor of 2.
Cancel the common factor.
2v2=-92
Divide v by 1.
v=-92
v=-92
Move the negative in front of the fraction.
v=-92
v=-92
v=-92
The final solution is all the values that make (v-4)(2v+9)=0 true.
v=4,-92
The result can be shown in multiple forms.
Exact Form:
v=4,-92
Decimal Form:
v=4,-4.5
Mixed Number Form:
v=4,-412
Solve for v 2v^2+v-36=0

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