6z^2+12z=5

Solution for 6z^2+12z=5 equation:

Simplifying
6z2 + 12z = 5

Reorder the terms:
12z + 6z2 = 5

Solving
12z + 6z2 = 5

Solving for variable 'z'.

Reorder the terms:
-5 + 12z + 6z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 12z + 6z2 = 0

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

Divide each side by '6'.
-0.8333333333 + 2z + z2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2z + 0.8333333333 + z2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2z + z2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2z + z2 = 0 + 0.8333333333
2z + z2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
2z + z2 = 0.8333333333

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 = 0.8333333333 + 1

Reorder the terms:
1 + 2z + z2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + 2z + z2 = 1.8333333333

Factor a perfect square on the left side:
(z + 1)(z + 1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(z + 1) equal to 1.354006401 and -1.354006401.

Subproblem 1
z + 1 = 1.354006401

Simplifying
z + 1 = 1.354006401

Reorder the terms:
1 + z = 1.354006401

Solving
1 + z = 1.354006401

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 = 1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + z = 1.354006401 + -1
z = 1.354006401 + -1

Combine like terms: 1.354006401 + -1 = 0.354006401
z = 0.354006401

Simplifying
z = 0.354006401

Subproblem 2
z + 1 = -1.354006401

Simplifying
z + 1 = -1.354006401

Reorder the terms:
1 + z = -1.354006401

Solving
1 + z = -1.354006401

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 = -1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + z = -1.354006401 + -1
z = -1.354006401 + -1

Combine like terms: -1.354006401 + -1 = -2.354006401
z = -2.354006401

Simplifying
z = -2.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.354006401, -2.354006401}