# Solve for z y=2z^2+7z+6 y=2z2+7z+6
Rewrite the equation as 2z2+7z+6=y.
2z2+7z+6=y
Move y to the left side of the equation by subtracting it from both sides.
2z2+7z+6-y=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=7, and c=6-y into the quadratic formula and solve for z.
-7±72-4⋅(2⋅(6-y))2⋅2
Simplify.
Simplify the numerator.
Raise 7 to the power of 2.
z=-7±49-4⋅(2⋅(6-y))2⋅2
Apply the distributive property.
z=-7±49-4⋅(2⋅6+2(-y))2⋅2
Multiply 2 by 6.
z=-7±49-4⋅(12+2(-y))2⋅2
Multiply -1 by 2.
z=-7±49-4⋅(12-2y)2⋅2
Apply the distributive property.
z=-7±49-4⋅12-4(-2y)2⋅2
Multiply -4 by 12.
z=-7±49-48-4(-2y)2⋅2
Multiply -2 by -4.
z=-7±49-48+8y2⋅2
Subtract 48 from 49.
z=-7±1+8y2⋅2
z=-7±1+8y2⋅2
Multiply 2 by 2.
z=-7±1+8y4
z=-7±1+8y4
The final answer is the combination of both solutions.
z=-7-1+8y4
z=-7+8y+14
Solve for z y=2z^2+7z+6

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