2z2-5z-7=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⋅-7=-14 and whose sum is b=-5.

Factor -5 out of -5z.

2z2-5z-7=0

Rewrite -5 as 2 plus -7

2z2+(2-7)z-7=0

Apply the distributive property.

2z2+2z-7z-7=0

2z2+2z-7z-7=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2z2+2z)-7z-7=0

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

2z(z+1)-7(z+1)=0

2z(z+1)-7(z+1)=0

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

(z+1)(2z-7)=0

(z+1)(2z-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.

z+1=0

2z-7=0

Set the first factor equal to 0.

z+1=0

Subtract 1 from both sides of the equation.

z=-1

z=-1

Set the next factor equal to 0.

2z-7=0

Add 7 to both sides of the equation.

2z=7

Divide each term by 2 and simplify.

Divide each term in 2z=7 by 2.

2z2=72

Cancel the common factor of 2.

Cancel the common factor.

2z2=72

Divide z by 1.

z=72

z=72

z=72

z=72

The final solution is all the values that make (z+1)(2z-7)=0 true.

z=-1,72

The result can be shown in multiple forms.

Exact Form:

z=-1,72

Decimal Form:

z=-1,3.5

Mixed Number Form:

z=-1,312

Solve for z 2z^2-5z-7=0