6z^2+12z=8z-5

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Solution for 6z^2+12z=8z-5 equation: 


Simplifying
6z2 + 12z = 8z + -5

Reorder the terms:
12z + 6z2 = 8z + -5

Reorder the terms:
12z + 6z2 = -5 + 8z

Solving
12z + 6z2 = -5 + 8z

Solving for variable 'z'.

Reorder the terms:
5 + 12z + -8z + 6z2 = -5 + 8z + 5 + -8z

Combine like terms: 12z + -8z = 4z
5 + 4z + 6z2 = -5 + 8z + 5 + -8z

Reorder the terms:
5 + 4z + 6z2 = -5 + 5 + 8z + -8z

Combine like terms: -5 + 5 = 0
5 + 4z + 6z2 = 0 + 8z + -8z
5 + 4z + 6z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
5 + 4z + 6z2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.8333333333 + 0.6666666667z + z2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 0.6666666667z + -0.8333333333 + z2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 0.6666666667z + z2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 0.6666666667z + z2 = 0 + -0.8333333333
0.6666666667z + z2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
0.6666666667z + z2 = -0.8333333333

The z term is 0.6666666667z.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667z + 0.1111111112 + z2 = -0.8333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667z + z2 = -0.8333333333 + 0.1111111112

Combine like terms: -0.8333333333 + 0.1111111112 = -0.7222222221
0.1111111112 + 0.6666666667z + z2 = -0.7222222221

Factor a perfect square on the left side:
(z + 0.3333333334)(z + 0.3333333334) = -0.7222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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