6(4z-1)2(z+4)=5(z+1)

Solution for 6(4z-1)2(z+4)=5(z+1) equation:

Simplifying
6(4z + -1) * 2(z + 4) = 5(z + 1)

Reorder the terms:
6(-1 + 4z) * 2(z + 4) = 5(z + 1)

Reorder the terms:
6(-1 + 4z) * 2(4 + z) = 5(z + 1)

Reorder the terms for easier multiplication:
6 * 2(-1 + 4z)(4 + z) = 5(z + 1)

Multiply 6 * 2
12(-1 + 4z)(4 + z) = 5(z + 1)

Multiply (-1 + 4z) * (4 + z)
12(-1(4 + z) + 4z * (4 + z)) = 5(z + 1)
12((4 * -1 + z * -1) + 4z * (4 + z)) = 5(z + 1)
12((-4 + -1z) + 4z * (4 + z)) = 5(z + 1)
12(-4 + -1z + (4 * 4z + z * 4z)) = 5(z + 1)
12(-4 + -1z + (16z + 4z2)) = 5(z + 1)

Combine like terms: -1z + 16z = 15z
12(-4 + 15z + 4z2) = 5(z + 1)
(-4 * 12 + 15z * 12 + 4z2 * 12) = 5(z + 1)
(-48 + 180z + 48z2) = 5(z + 1)

Reorder the terms:
-48 + 180z + 48z2 = 5(1 + z)
-48 + 180z + 48z2 = (1 * 5 + z * 5)
-48 + 180z + 48z2 = (5 + 5z)

Solving
-48 + 180z + 48z2 = 5 + 5z

Solving for variable 'z'.

Reorder the terms:
-48 + -5 + 180z + -5z + 48z2 = 5 + 5z + -5 + -5z

Combine like terms: -48 + -5 = -53
-53 + 180z + -5z + 48z2 = 5 + 5z + -5 + -5z

Combine like terms: 180z + -5z = 175z
-53 + 175z + 48z2 = 5 + 5z + -5 + -5z

Reorder the terms:
-53 + 175z + 48z2 = 5 + -5 + 5z + -5z

Combine like terms: 5 + -5 = 0
-53 + 175z + 48z2 = 0 + 5z + -5z
-53 + 175z + 48z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-53 + 175z + 48z2 = 0

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

Divide each side by '48'.
-1.104166667 + 3.645833333z + z2 = 0

Move the constant term to the right:

Add '1.104166667' to each side of the equation.
-1.104166667 + 3.645833333z + 1.104166667 + z2 = 0 + 1.104166667

Reorder the terms:
-1.104166667 + 1.104166667 + 3.645833333z + z2 = 0 + 1.104166667

Combine like terms: -1.104166667 + 1.104166667 = 0.000000000
0.000000000 + 3.645833333z + z2 = 0 + 1.104166667
3.645833333z + z2 = 0 + 1.104166667

Combine like terms: 0 + 1.104166667 = 1.104166667
3.645833333z + z2 = 1.104166667

The z term is 3.645833333z.  Take half its coefficient (1.822916667).
Square it (3.323025175) and add it to both sides.

Add '3.323025175' to each side of the equation.
3.645833333z + 3.323025175 + z2 = 1.104166667 + 3.323025175

Reorder the terms:
3.323025175 + 3.645833333z + z2 = 1.104166667 + 3.323025175

Combine like terms: 1.104166667 + 3.323025175 = 4.427191842
3.323025175 + 3.645833333z + z2 = 4.427191842

Factor a perfect square on the left side:
(z + 1.822916667)(z + 1.822916667) = 4.427191842

Calculate the square root of the right side: 2.104089314

Break this problem into two subproblems by setting 
(z + 1.822916667) equal to 2.104089314 and -2.104089314.

Subproblem 1
z + 1.822916667 = 2.104089314

Simplifying
z + 1.822916667 = 2.104089314

Reorder the terms:
1.822916667 + z = 2.104089314

Solving
1.822916667 + z = 2.104089314

Solving for variable 'z'.

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

Add '-1.822916667' to each side of the equation.
1.822916667 + -1.822916667 + z = 2.104089314 + -1.822916667

Combine like terms: 1.822916667 + -1.822916667 = 0.000000000
0.000000000 + z = 2.104089314 + -1.822916667
z = 2.104089314 + -1.822916667

Combine like terms: 2.104089314 + -1.822916667 = 0.281172647
z = 0.281172647

Simplifying
z = 0.281172647

Subproblem 2
z + 1.822916667 = -2.104089314

Simplifying
z + 1.822916667 = -2.104089314

Reorder the terms:
1.822916667 + z = -2.104089314

Solving
1.822916667 + z = -2.104089314

Solving for variable 'z'.

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

Add '-1.822916667' to each side of the equation.
1.822916667 + -1.822916667 + z = -2.104089314 + -1.822916667

Combine like terms: 1.822916667 + -1.822916667 = 0.000000000
0.000000000 + z = -2.104089314 + -1.822916667
z = -2.104089314 + -1.822916667

Combine like terms: -2.104089314 + -1.822916667 = -3.927005981
z = -3.927005981

Simplifying
z = -3.927005981

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.281172647, -3.927005981}