# Solve for z 2z^2-5z-7=0 2z2-5z-7=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⋅-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 and solve.
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 and solve.
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

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