6z^2+17z-3=6z+3

Solution for 6z^2+17z-3=6z+3 equation:

Simplifying
6z2 + 17z + -3 = 6z + 3

Reorder the terms:
-3 + 17z + 6z2 = 6z + 3

Reorder the terms:
-3 + 17z + 6z2 = 3 + 6z

Solving
-3 + 17z + 6z2 = 3 + 6z

Solving for variable 'z'.

Reorder the terms:
-3 + -3 + 17z + -6z + 6z2 = 3 + 6z + -3 + -6z

Combine like terms: -3 + -3 = -6
-6 + 17z + -6z + 6z2 = 3 + 6z + -3 + -6z

Combine like terms: 17z + -6z = 11z
-6 + 11z + 6z2 = 3 + 6z + -3 + -6z

Reorder the terms:
-6 + 11z + 6z2 = 3 + -3 + 6z + -6z

Combine like terms: 3 + -3 = 0
-6 + 11z + 6z2 = 0 + 6z + -6z
-6 + 11z + 6z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-6 + 11z + 6z2 = 0

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

Divide each side by '6'.
-1 + 1.833333333z + z2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.833333333z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.833333333z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.833333333z + z2 = 0 + 1
1.833333333z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.833333333z + z2 = 1

The z term is 1.833333333z.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333z + 0.8402777775 + z2 = 1 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333z + z2 = 1 + 0.8402777775

Combine like terms: 1 + 0.8402777775 = 1.8402777775
0.8402777775 + 1.833333333z + z2 = 1.8402777775

Factor a perfect square on the left side:
(z + 0.9166666665)(z + 0.9166666665) = 1.8402777775

Calculate the square root of the right side: 1.356568383

Break this problem into two subproblems by setting 
(z + 0.9166666665) equal to 1.356568383 and -1.356568383.

Subproblem 1
z + 0.9166666665 = 1.356568383

Simplifying
z + 0.9166666665 = 1.356568383

Reorder the terms:
0.9166666665 + z = 1.356568383

Solving
0.9166666665 + z = 1.356568383

Solving for variable 'z'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + z = 1.356568383 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + z = 1.356568383 + -0.9166666665
z = 1.356568383 + -0.9166666665

Combine like terms: 1.356568383 + -0.9166666665 = 0.4399017165
z = 0.4399017165

Simplifying
z = 0.4399017165

Subproblem 2
z + 0.9166666665 = -1.356568383

Simplifying
z + 0.9166666665 = -1.356568383

Reorder the terms:
0.9166666665 + z = -1.356568383

Solving
0.9166666665 + z = -1.356568383

Solving for variable 'z'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + z = -1.356568383 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + z = -1.356568383 + -0.9166666665
z = -1.356568383 + -0.9166666665

Combine like terms: -1.356568383 + -0.9166666665 = -2.2732350495
z = -2.2732350495

Simplifying
z = -2.2732350495

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.4399017165, -2.2732350495}