-53=-3(3z+3)3z

Solution for -53=-3(3z+3)3z equation:

Simplifying
-53 = -3(3z + 3) * 3z

Reorder the terms:
-53 = -3(3 + 3z) * 3z

Reorder the terms for easier multiplication:
-53 = -3 * 3z(3 + 3z)

Multiply -3 * 3
-53 = -9z(3 + 3z)
-53 = (3 * -9z + 3z * -9z)
-53 = (-27z + -27z2)

Solving
-53 = -27z + -27z2

Solving for variable 'z'.

Reorder the terms:
-53 + 27z + 27z2 = -27z + 27z + -27z2 + 27z2

Combine like terms: -27z + 27z = 0
-53 + 27z + 27z2 = 0 + -27z2 + 27z2
-53 + 27z + 27z2 = -27z2 + 27z2

Combine like terms: -27z2 + 27z2 = 0
-53 + 27z + 27z2 = 0

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

Divide each side by '27'.
-1.962962963 + z + z2 = 0

Move the constant term to the right:

Add '1.962962963' to each side of the equation.
-1.962962963 + z + 1.962962963 + z2 = 0 + 1.962962963

Reorder the terms:
-1.962962963 + 1.962962963 + z + z2 = 0 + 1.962962963

Combine like terms: -1.962962963 + 1.962962963 = 0.000000000
0.000000000 + z + z2 = 0 + 1.962962963
z + z2 = 0 + 1.962962963

Combine like terms: 0 + 1.962962963 = 1.962962963
z + z2 = 1.962962963

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.
 + 0.25 + z2 = 1.962962963 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z2 = 1.962962963 + 0.25

Combine like terms: 1.962962963 + 0.25 = 2.212962963
1.25 + z2 = 2.212962963

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 2.212962963

Calculate the square root of the right side: 1.487603093

Break this problem into two subproblems by setting 
(z + 0.5) equal to 1.487603093 and -1.487603093.

Subproblem 1
z + 0.5 = 1.487603093

Simplifying
z + 0.5 = 1.487603093

Reorder the terms:
0.5 + z = 1.487603093

Solving
0.5 + z = 1.487603093

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 = 1.487603093 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = 1.487603093 + -0.5
z = 1.487603093 + -0.5

Combine like terms: 1.487603093 + -0.5 = 0.987603093
z = 0.987603093

Simplifying
z = 0.987603093

Subproblem 2
z + 0.5 = -1.487603093

Simplifying
z + 0.5 = -1.487603093

Reorder the terms:
0.5 + z = -1.487603093

Solving
0.5 + z = -1.487603093

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 = -1.487603093 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z = -1.487603093 + -0.5
z = -1.487603093 + -0.5

Combine like terms: -1.487603093 + -0.5 = -1.987603093
z = -1.987603093

Simplifying
z = -1.987603093

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.987603093, -1.987603093}