# Solve for z 2z^2+3z+7=9

2z2+3z+7=9
Move 9 to the left side of the equation by subtracting it from both sides.
2z2+3z+7-9=0
Subtract 9 from 7.
2z2+3z-2=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⋅-2=-4 and whose sum is b=3.
Factor 3 out of 3z.
2z2+3(z)-2=0
Rewrite 3 as -1 plus 4
2z2+(-1+4)z-2=0
Apply the distributive property.
2z2-1z+4z-2=0
2z2-1z+4z-2=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2z2-1z)+4z-2=0
Factor out the greatest common factor (GCF) from each group.
z(2z-1)+2(2z-1)=0
z(2z-1)+2(2z-1)=0
Factor the polynomial by factoring out the greatest common factor, 2z-1.
(2z-1)(z+2)=0
(2z-1)(z+2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2z-1=0
z+2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
2z-1=0
Add 1 to both sides of the equation.
2z=1
Divide each term by 2 and simplify.
Divide each term in 2z=1 by 2.
2z2=12
Cancel the common factor of 2.
Cancel the common factor.
2z2=12
Divide z by 1.
z=12
z=12
z=12
z=12
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
z+2=0
Subtract 2 from both sides of the equation.
z=-2
z=-2
The final solution is all the values that make (2z-1)(z+2)=0 true.
z=12,-2
The result can be shown in multiple forms.
Exact Form:
z=12,-2
Decimal Form:
z=0.5,-2
Solve for z 2z^2+3z+7=9

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