3(6z-1)2(z+3)=7(z+1)

Solution for 3(6z-1)2(z+3)=7(z+1) equation:

Simplifying
3(6z + -1) * 2(z + 3) = 7(z + 1)

Reorder the terms:
3(-1 + 6z) * 2(z + 3) = 7(z + 1)

Reorder the terms:
3(-1 + 6z) * 2(3 + z) = 7(z + 1)

Reorder the terms for easier multiplication:
3 * 2(-1 + 6z)(3 + z) = 7(z + 1)

Multiply 3 * 2
6(-1 + 6z)(3 + z) = 7(z + 1)

Multiply (-1 + 6z) * (3 + z)
6(-1(3 + z) + 6z * (3 + z)) = 7(z + 1)
6((3 * -1 + z * -1) + 6z * (3 + z)) = 7(z + 1)
6((-3 + -1z) + 6z * (3 + z)) = 7(z + 1)
6(-3 + -1z + (3 * 6z + z * 6z)) = 7(z + 1)
6(-3 + -1z + (18z + 6z2)) = 7(z + 1)

Combine like terms: -1z + 18z = 17z
6(-3 + 17z + 6z2) = 7(z + 1)
(-3 * 6 + 17z * 6 + 6z2 * 6) = 7(z + 1)
(-18 + 102z + 36z2) = 7(z + 1)

Reorder the terms:
-18 + 102z + 36z2 = 7(1 + z)
-18 + 102z + 36z2 = (1 * 7 + z * 7)
-18 + 102z + 36z2 = (7 + 7z)

Solving
-18 + 102z + 36z2 = 7 + 7z

Solving for variable 'z'.

Reorder the terms:
-18 + -7 + 102z + -7z + 36z2 = 7 + 7z + -7 + -7z

Combine like terms: -18 + -7 = -25
-25 + 102z + -7z + 36z2 = 7 + 7z + -7 + -7z

Combine like terms: 102z + -7z = 95z
-25 + 95z + 36z2 = 7 + 7z + -7 + -7z

Reorder the terms:
-25 + 95z + 36z2 = 7 + -7 + 7z + -7z

Combine like terms: 7 + -7 = 0
-25 + 95z + 36z2 = 0 + 7z + -7z
-25 + 95z + 36z2 = 7z + -7z

Combine like terms: 7z + -7z = 0
-25 + 95z + 36z2 = 0

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

Divide each side by '36'.
-0.6944444444 + 2.638888889z + z2 = 0

Move the constant term to the right:

Add '0.6944444444' to each side of the equation.
-0.6944444444 + 2.638888889z + 0.6944444444 + z2 = 0 + 0.6944444444

Reorder the terms:
-0.6944444444 + 0.6944444444 + 2.638888889z + z2 = 0 + 0.6944444444

Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000
0.0000000000 + 2.638888889z + z2 = 0 + 0.6944444444
2.638888889z + z2 = 0 + 0.6944444444

Combine like terms: 0 + 0.6944444444 = 0.6944444444
2.638888889z + z2 = 0.6944444444

The z term is 2.638888889z.  Take half its coefficient (1.319444445).
Square it (1.740933643) and add it to both sides.

Add '1.740933643' to each side of the equation.
2.638888889z + 1.740933643 + z2 = 0.6944444444 + 1.740933643

Reorder the terms:
1.740933643 + 2.638888889z + z2 = 0.6944444444 + 1.740933643

Combine like terms: 0.6944444444 + 1.740933643 = 2.4353780874
1.740933643 + 2.638888889z + z2 = 2.4353780874

Factor a perfect square on the left side:
(z + 1.319444445)(z + 1.319444445) = 2.4353780874

Calculate the square root of the right side: 1.560569796

Break this problem into two subproblems by setting 
(z + 1.319444445) equal to 1.560569796 and -1.560569796.

Subproblem 1
z + 1.319444445 = 1.560569796

Simplifying
z + 1.319444445 = 1.560569796

Reorder the terms:
1.319444445 + z = 1.560569796

Solving
1.319444445 + z = 1.560569796

Solving for variable 'z'.

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

Add '-1.319444445' to each side of the equation.
1.319444445 + -1.319444445 + z = 1.560569796 + -1.319444445

Combine like terms: 1.319444445 + -1.319444445 = 0.000000000
0.000000000 + z = 1.560569796 + -1.319444445
z = 1.560569796 + -1.319444445

Combine like terms: 1.560569796 + -1.319444445 = 0.241125351
z = 0.241125351

Simplifying
z = 0.241125351

Subproblem 2
z + 1.319444445 = -1.560569796

Simplifying
z + 1.319444445 = -1.560569796

Reorder the terms:
1.319444445 + z = -1.560569796

Solving
1.319444445 + z = -1.560569796

Solving for variable 'z'.

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

Add '-1.319444445' to each side of the equation.
1.319444445 + -1.319444445 + z = -1.560569796 + -1.319444445

Combine like terms: 1.319444445 + -1.319444445 = 0.000000000
0.000000000 + z = -1.560569796 + -1.319444445
z = -1.560569796 + -1.319444445

Combine like terms: -1.560569796 + -1.319444445 = -2.880014241
z = -2.880014241

Simplifying
z = -2.880014241

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.241125351, -2.880014241}