# Solve for z h(3z)=2*(3z^2)-6 h(3z)=2⋅(3z2)-6
Rewrite using the commutative property of multiplication.
3hz=2⋅(3z2)-6
Multiply 3 by 2.
3hz=6z2-6
Subtract 6z2 from both sides of the equation.
3hz-6z2=-6
Move 6 to the left side of the equation by adding it to both sides.
3hz-6z2+6=0
Factor the left side of the equation.
Factor 3 out of 3hz-6z2+6.
Factor 3 out of 3hz.
3(hz)-6z2+6
Factor 3 out of -6z2.
3(hz)+3(-2z2)+6
Factor 3 out of 6.
3(hz)+3(-2z2)+3⋅2
Factor 3 out of 3(hz)+3(-2z2).
3(hz-2z2)+3⋅2
Factor 3 out of 3(hz-2z2)+3⋅2.
3(hz-2z2+2)
3(hz-2z2+2)
Replace the left side with the factored expression.
3(hz-2z2+2)=0
3(hz-2z2+2)=0
Divide each term by 3 and simplify.
Divide each term in 3(hz-2z2+2)=0 by 3.
3(hz-2z2+2)3=03
Cancel the common factor of 3.
Cancel the common factor.
3(hz-2z2+2)3=03
Divide hz-2z2+2 by 1.
hz-2z2+2=03
hz-2z2+2=03
Divide 0 by 3.
hz-2z2+2=0
hz-2z2+2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=-2, b=h, and c=2 into the quadratic formula and solve for z.
-h±h2-4⋅(-2⋅2)2⋅-2
Simplify.
Simplify the numerator.
Multiply -2 by 2.
z=-h±h2-4⋅-42⋅-2
Multiply -4 by -4.
z=-h±h2+162⋅-2
z=-h±h2+162⋅-2
Multiply 2 by -2.
z=-h±h2+16-4
Simplify -h±h2+16-4.
z=h±h2+164
z=h±h2+164
The final answer is the combination of both solutions.
z=h+h2+164
z=h-h2+164
Solve for z h(3z)=2*(3z^2)-6

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