3z^2-6z=141

Solution for 3z^2-6z=141 equation:

Simplifying
3z2 + -6z = 141

Reorder the terms:
-6z + 3z2 = 141

Solving
-6z + 3z2 = 141

Solving for variable 'z'.

Reorder the terms:
-141 + -6z + 3z2 = 141 + -141

Combine like terms: 141 + -141 = 0
-141 + -6z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-47 + -2z + z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-47 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
-47 + -2z + z2 = 0

Solving
-47 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -2z + 47 + z2 = 0 + 47

Reorder the terms:
-47 + 47 + -2z + z2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -2z + z2 = 0 + 47
-2z + z2 = 0 + 47

Combine like terms: 0 + 47 = 47
-2z + z2 = 47

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = 47 + 1

Reorder the terms:
1 + -2z + z2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + -2z + z2 = 48

Factor a perfect square on the left side:
(z + -1)(z + -1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(z + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1
z + -1 = 6.92820323

Simplifying
z + -1 = 6.92820323

Reorder the terms:
-1 + z = 6.92820323

Solving
-1 + z = 6.92820323

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = 6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + z = 6.92820323 + 1
z = 6.92820323 + 1

Combine like terms: 6.92820323 + 1 = 7.92820323
z = 7.92820323

Simplifying
z = 7.92820323

Subproblem 2
z + -1 = -6.92820323

Simplifying
z + -1 = -6.92820323

Reorder the terms:
-1 + z = -6.92820323

Solving
-1 + z = -6.92820323

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z = -6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + z = -6.92820323 + 1
z = -6.92820323 + 1

Combine like terms: -6.92820323 + 1 = -5.92820323
z = -5.92820323

Simplifying
z = -5.92820323

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {7.92820323, -5.92820323}
Solution
z = {7.92820323, -5.92820323}