3z^2-4z=-7

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Solution for 3z^2-4z=-7 equation: 


Simplifying
3z2 + -4z = -7

Reorder the terms:
-4z + 3z2 = -7

Solving
-4z + 3z2 = -7

Solving for variable 'z'.

Reorder the terms:
7 + -4z + 3z2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + -4z + 3z2 = 0

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

Divide each side by '3'.
2.333333333 + -1.333333333z + z2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -1.333333333z + -2.333333333 + z2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -1.333333333z + z2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -1.333333333z + z2 = 0 + -2.333333333
-1.333333333z + z2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-1.333333333z + z2 = -2.333333333

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 = -2.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333z + z2 = -2.333333333 + 0.4444444442

Combine like terms: -2.333333333 + 0.4444444442 = -1.8888888888
0.4444444442 + -1.333333333z + z2 = -1.8888888888

Factor a perfect square on the left side:
(z + -0.6666666665)(z + -0.6666666665) = -1.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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