3z(z)+3z-9=0

Solution for 3z(z)+3z-9=0 equation:

Simplifying
3z(z) + 3z + -9 = 0

Multiply z * z
3z2 + 3z + -9 = 0

Reorder the terms:
-9 + 3z + 3z2 = 0

Solving
-9 + 3z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + z + z2)' equal to zero and attempt to solve:

Simplifying
-3 + z + z2 = 0

Solving
-3 + z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + z + z2 = 0 + 3

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

Combine like terms: 0 + 3 = 3
z + z2 = 3

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = 3 + 0.25

Reorder the terms:
0.25 + z + z2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + z + z2 = 3.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(z + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
z + 0.5 = 1.802775638

Simplifying
z + 0.5 = 1.802775638

Reorder the terms:
0.5 + z = 1.802775638

Solving
0.5 + z = 1.802775638

Solving for variable 'z'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + z = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = 1.802775638 + -0.5
z = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
z = 1.302775638

Simplifying
z = 1.302775638

Subproblem 2
z + 0.5 = -1.802775638

Simplifying
z + 0.5 = -1.802775638

Reorder the terms:
0.5 + z = -1.802775638

Solving
0.5 + z = -1.802775638

Solving for variable 'z'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + z = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = -1.802775638 + -0.5
z = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
z = -2.302775638

Simplifying
z = -2.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.302775638, -2.302775638}
Solution
z = {1.302775638, -2.302775638}