z(4-3z)+3=-6(z-4)-8

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Solution for z(4-3z)+3=-6(z-4)-8 equation: 


Simplifying
z(4 + -3z) + 3 = -6(z + -4) + -8
(4 * z + -3z * z) + 3 = -6(z + -4) + -8
(4z + -3z2) + 3 = -6(z + -4) + -8

Reorder the terms:
3 + 4z + -3z2 = -6(z + -4) + -8

Reorder the terms:
3 + 4z + -3z2 = -6(-4 + z) + -8
3 + 4z + -3z2 = (-4 * -6 + z * -6) + -8
3 + 4z + -3z2 = (24 + -6z) + -8

Reorder the terms:
3 + 4z + -3z2 = 24 + -8 + -6z

Combine like terms: 24 + -8 = 16
3 + 4z + -3z2 = 16 + -6z

Solving
3 + 4z + -3z2 = 16 + -6z

Solving for variable 'z'.

Reorder the terms:
3 + -16 + 4z + 6z + -3z2 = 16 + -6z + -16 + 6z

Combine like terms: 3 + -16 = -13
-13 + 4z + 6z + -3z2 = 16 + -6z + -16 + 6z

Combine like terms: 4z + 6z = 10z
-13 + 10z + -3z2 = 16 + -6z + -16 + 6z

Reorder the terms:
-13 + 10z + -3z2 = 16 + -16 + -6z + 6z

Combine like terms: 16 + -16 = 0
-13 + 10z + -3z2 = 0 + -6z + 6z
-13 + 10z + -3z2 = -6z + 6z

Combine like terms: -6z + 6z = 0
-13 + 10z + -3z2 = 0

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

Divide each side by '-3'.
4.333333333 + -3.333333333z + z2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + -3.333333333z + -4.333333333 + z2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + -3.333333333z + z2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + -3.333333333z + z2 = 0 + -4.333333333
-3.333333333z + z2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
-3.333333333z + z2 = -4.333333333

The z term is -3.333333333z.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333z + 2.777777779 + z2 = -4.333333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333z + z2 = -4.333333333 + 2.777777779

Combine like terms: -4.333333333 + 2.777777779 = -1.555555554
2.777777779 + -3.333333333z + z2 = -1.555555554

Factor a perfect square on the left side:
(z + -1.666666667)(z + -1.666666667) = -1.555555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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