136=2(3z+3)(4z+2)

Solution for 136=2(3z+3)(4z+2) equation:

Simplifying
136 = 2(3z + 3)(4z + 2)

Reorder the terms:
136 = 2(3 + 3z)(4z + 2)

Reorder the terms:
136 = 2(3 + 3z)(2 + 4z)

Multiply (3 + 3z) * (2 + 4z)
136 = 2(3(2 + 4z) + 3z * (2 + 4z))
136 = 2((2 * 3 + 4z * 3) + 3z * (2 + 4z))
136 = 2((6 + 12z) + 3z * (2 + 4z))
136 = 2(6 + 12z + (2 * 3z + 4z * 3z))
136 = 2(6 + 12z + (6z + 12z2))

Combine like terms: 12z + 6z = 18z
136 = 2(6 + 18z + 12z2)
136 = (6 * 2 + 18z * 2 + 12z2 * 2)
136 = (12 + 36z + 24z2)

Solving
136 = 12 + 36z + 24z2

Solving for variable 'z'.

Combine like terms: 136 + -12 = 124
124 + -36z + -24z2 = 12 + 36z + 24z2 + -12 + -36z + -24z2

Reorder the terms:
124 + -36z + -24z2 = 12 + -12 + 36z + -36z + 24z2 + -24z2

Combine like terms: 12 + -12 = 0
124 + -36z + -24z2 = 0 + 36z + -36z + 24z2 + -24z2
124 + -36z + -24z2 = 36z + -36z + 24z2 + -24z2

Combine like terms: 36z + -36z = 0
124 + -36z + -24z2 = 0 + 24z2 + -24z2
124 + -36z + -24z2 = 24z2 + -24z2

Combine like terms: 24z2 + -24z2 = 0
124 + -36z + -24z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(31 + -9z + -6z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(31 + -9z + -6z2)' equal to zero and attempt to solve:

Simplifying
31 + -9z + -6z2 = 0

Solving
31 + -9z + -6z2 = 0

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

Divide each side by '-6'.
-5.166666667 + 1.5z + z2 = 0

Move the constant term to the right:

Add '5.166666667' to each side of the equation.
-5.166666667 + 1.5z + 5.166666667 + z2 = 0 + 5.166666667

Reorder the terms:
-5.166666667 + 5.166666667 + 1.5z + z2 = 0 + 5.166666667

Combine like terms: -5.166666667 + 5.166666667 = 0.000000000
0.000000000 + 1.5z + z2 = 0 + 5.166666667
1.5z + z2 = 0 + 5.166666667

Combine like terms: 0 + 5.166666667 = 5.166666667
1.5z + z2 = 5.166666667

The z term is 1.5z.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5z + 0.5625 + z2 = 5.166666667 + 0.5625

Reorder the terms:
0.5625 + 1.5z + z2 = 5.166666667 + 0.5625

Combine like terms: 5.166666667 + 0.5625 = 5.729166667
0.5625 + 1.5z + z2 = 5.729166667

Factor a perfect square on the left side:
(z + 0.75)(z + 0.75) = 5.729166667

Calculate the square root of the right side: 2.393567769

Break this problem into two subproblems by setting 
(z + 0.75) equal to 2.393567769 and -2.393567769.

Subproblem 1
z + 0.75 = 2.393567769

Simplifying
z + 0.75 = 2.393567769

Reorder the terms:
0.75 + z = 2.393567769

Solving
0.75 + z = 2.393567769

Solving for variable 'z'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + z = 2.393567769 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + z = 2.393567769 + -0.75
z = 2.393567769 + -0.75

Combine like terms: 2.393567769 + -0.75 = 1.643567769
z = 1.643567769

Simplifying
z = 1.643567769

Subproblem 2
z + 0.75 = -2.393567769

Simplifying
z + 0.75 = -2.393567769

Reorder the terms:
0.75 + z = -2.393567769

Solving
0.75 + z = -2.393567769

Solving for variable 'z'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + z = -2.393567769 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + z = -2.393567769 + -0.75
z = -2.393567769 + -0.75

Combine like terms: -2.393567769 + -0.75 = -3.143567769
z = -3.143567769

Simplifying
z = -3.143567769

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.643567769, -3.143567769}
Solution
z = {1.643567769, -3.143567769}