3z^2+4z=8z-5

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Solution for 3z^2+4z=8z-5 equation:


Simplifying
3z2 + 4z = 8z + -5

Reorder the terms:
4z + 3z2 = 8z + -5

Reorder the terms:
4z + 3z2 = -5 + 8z

Solving
4z + 3z2 = -5 + 8z

Solving for variable 'z'.

Reorder the terms:
5 + 4z + -8z + 3z2 = -5 + 8z + 5 + -8z

Combine like terms: 4z + -8z = -4z
5 + -4z + 3z2 = -5 + 8z + 5 + -8z

Reorder the terms:
5 + -4z + 3z2 = -5 + 5 + 8z + -8z

Combine like terms: -5 + 5 = 0
5 + -4z + 3z2 = 0 + 8z + -8z
5 + -4z + 3z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
5 + -4z + 3z2 = 0

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

Divide each side by '3'.
1.666666667 + -1.333333333z + z2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.333333333z + -1.666666667 + z2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1.333333333z + z2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1.333333333z + z2 = 0 + -1.666666667
-1.333333333z + z2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1.333333333z + z2 = -1.666666667

The z term is -1.333333333z.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333z + 0.4444444442 + z2 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333z + z2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + -1.333333333z + z2 = -1.2222222228

Factor a perfect square on the left side:
(z + -0.6666666665)(z + -0.6666666665) = -1.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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