2v2+v-36=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⋅-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.

v-4=0

Add 4 to both sides of the equation.

v=4

v=4

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