6(3-2z)11z-4=

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Solution for 6(3-2z)11z-4= equation: 


Simplifying
6(3 + -2z) * 11z + -4 = 0

Reorder the terms for easier multiplication:
6 * 11z(3 + -2z) + -4 = 0

Multiply 6 * 11
66z(3 + -2z) + -4 = 0
(3 * 66z + -2z * 66z) + -4 = 0
(198z + -132z2) + -4 = 0

Reorder the terms:
-4 + 198z + -132z2 = 0

Solving
-4 + 198z + -132z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 99z + -66z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 99z + -66z2)' equal to zero and attempt to solve:

Simplifying
-2 + 99z + -66z2 = 0

Solving
-2 + 99z + -66z2 = 0

Begin completing the square.  Divide all terms by
-66 the coefficient of the squared term: 

Divide each side by '-66'.
0.0303030303 + -1.5z + z2 = 0

Move the constant term to the right:

Add '-0.0303030303' to each side of the equation.
0.0303030303 + -1.5z + -0.0303030303 + z2 = 0 + -0.0303030303

Reorder the terms:
0.0303030303 + -0.0303030303 + -1.5z + z2 = 0 + -0.0303030303

Combine like terms: 0.0303030303 + -0.0303030303 = 0.0000000000
0.0000000000 + -1.5z + z2 = 0 + -0.0303030303
-1.5z + z2 = 0 + -0.0303030303

Combine like terms: 0 + -0.0303030303 = -0.0303030303
-1.5z + z2 = -0.0303030303

The z term is -1.5z.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5z + 0.5625 + z2 = -0.0303030303 + 0.5625

Reorder the terms:
0.5625 + -1.5z + z2 = -0.0303030303 + 0.5625

Combine like terms: -0.0303030303 + 0.5625 = 0.5321969697
0.5625 + -1.5z + z2 = 0.5321969697

Factor a perfect square on the left side:
(z + -0.75)(z + -0.75) = 0.5321969697

Calculate the square root of the right side: 0.729518313

Break this problem into two subproblems by setting 
(z + -0.75) equal to 0.729518313 and -0.729518313.


Subproblem 1
z + -0.75 = 0.729518313

Simplifying
z + -0.75 = 0.729518313

Reorder the terms:
-0.75 + z = 0.729518313

Solving
-0.75 + z = 0.729518313

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '0.75' to each side of the equation.
-0.75 + 0.75 + z = 0.729518313 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + z = 0.729518313 + 0.75
z = 0.729518313 + 0.75

Combine like terms: 0.729518313 + 0.75 = 1.479518313
z = 1.479518313

Simplifying
z = 1.479518313


Subproblem 2
z + -0.75 = -0.729518313

Simplifying
z + -0.75 = -0.729518313

Reorder the terms:
-0.75 + z = -0.729518313

Solving
-0.75 + z = -0.729518313

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '0.75' to each side of the equation.
-0.75 + 0.75 + z = -0.729518313 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + z = -0.729518313 + 0.75
z = -0.729518313 + 0.75

Combine like terms: -0.729518313 + 0.75 = 0.020481687
z = 0.020481687

Simplifying
z = 0.020481687


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.479518313, 0.020481687}
Solution
z = {1.479518313, 0.020481687}

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