3(4z-1)4(z+3)=3(z+1)

Solution for 3(4z-1)4(z+3)=3(z+1) equation:

Simplifying
3(4z + -1) * 4(z + 3) = 3(z + 1)

Reorder the terms:
3(-1 + 4z) * 4(z + 3) = 3(z + 1)

Reorder the terms:
3(-1 + 4z) * 4(3 + z) = 3(z + 1)

Reorder the terms for easier multiplication:
3 * 4(-1 + 4z)(3 + z) = 3(z + 1)

Multiply 3 * 4
12(-1 + 4z)(3 + z) = 3(z + 1)

Multiply (-1 + 4z) * (3 + z)
12(-1(3 + z) + 4z * (3 + z)) = 3(z + 1)
12((3 * -1 + z * -1) + 4z * (3 + z)) = 3(z + 1)
12((-3 + -1z) + 4z * (3 + z)) = 3(z + 1)
12(-3 + -1z + (3 * 4z + z * 4z)) = 3(z + 1)
12(-3 + -1z + (12z + 4z2)) = 3(z + 1)

Combine like terms: -1z + 12z = 11z
12(-3 + 11z + 4z2) = 3(z + 1)
(-3 * 12 + 11z * 12 + 4z2 * 12) = 3(z + 1)
(-36 + 132z + 48z2) = 3(z + 1)

Reorder the terms:
-36 + 132z + 48z2 = 3(1 + z)
-36 + 132z + 48z2 = (1 * 3 + z * 3)
-36 + 132z + 48z2 = (3 + 3z)

Solving
-36 + 132z + 48z2 = 3 + 3z

Solving for variable 'z'.

Reorder the terms:
-36 + -3 + 132z + -3z + 48z2 = 3 + 3z + -3 + -3z

Combine like terms: -36 + -3 = -39
-39 + 132z + -3z + 48z2 = 3 + 3z + -3 + -3z

Combine like terms: 132z + -3z = 129z
-39 + 129z + 48z2 = 3 + 3z + -3 + -3z

Reorder the terms:
-39 + 129z + 48z2 = 3 + -3 + 3z + -3z

Combine like terms: 3 + -3 = 0
-39 + 129z + 48z2 = 0 + 3z + -3z
-39 + 129z + 48z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
-39 + 129z + 48z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + 43z + 16z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-13 + 43z + 16z2)' equal to zero and attempt to solve:

Simplifying
-13 + 43z + 16z2 = 0

Solving
-13 + 43z + 16z2 = 0

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

Divide each side by '16'.
-0.8125 + 2.6875z + z2 = 0

Move the constant term to the right:

Add '0.8125' to each side of the equation.
-0.8125 + 2.6875z + 0.8125 + z2 = 0 + 0.8125

Reorder the terms:
-0.8125 + 0.8125 + 2.6875z + z2 = 0 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + 2.6875z + z2 = 0 + 0.8125
2.6875z + z2 = 0 + 0.8125

Combine like terms: 0 + 0.8125 = 0.8125
2.6875z + z2 = 0.8125

The z term is 2.6875z.  Take half its coefficient (1.34375).
Square it (1.805664063) and add it to both sides.

Add '1.805664063' to each side of the equation.
2.6875z + 1.805664063 + z2 = 0.8125 + 1.805664063

Reorder the terms:
1.805664063 + 2.6875z + z2 = 0.8125 + 1.805664063

Combine like terms: 0.8125 + 1.805664063 = 2.618164063
1.805664063 + 2.6875z + z2 = 2.618164063

Factor a perfect square on the left side:
(z + 1.34375)(z + 1.34375) = 2.618164063

Calculate the square root of the right side: 1.618074183

Break this problem into two subproblems by setting 
(z + 1.34375) equal to 1.618074183 and -1.618074183.

Subproblem 1
z + 1.34375 = 1.618074183

Simplifying
z + 1.34375 = 1.618074183

Reorder the terms:
1.34375 + z = 1.618074183

Solving
1.34375 + z = 1.618074183

Solving for variable 'z'.

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

Add '-1.34375' to each side of the equation.
1.34375 + -1.34375 + z = 1.618074183 + -1.34375

Combine like terms: 1.34375 + -1.34375 = 0.00000
0.00000 + z = 1.618074183 + -1.34375
z = 1.618074183 + -1.34375

Combine like terms: 1.618074183 + -1.34375 = 0.274324183
z = 0.274324183

Simplifying
z = 0.274324183

Subproblem 2
z + 1.34375 = -1.618074183

Simplifying
z + 1.34375 = -1.618074183

Reorder the terms:
1.34375 + z = -1.618074183

Solving
1.34375 + z = -1.618074183

Solving for variable 'z'.

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

Add '-1.34375' to each side of the equation.
1.34375 + -1.34375 + z = -1.618074183 + -1.34375

Combine like terms: 1.34375 + -1.34375 = 0.00000
0.00000 + z = -1.618074183 + -1.34375
z = -1.618074183 + -1.34375

Combine like terms: -1.618074183 + -1.34375 = -2.961824183
z = -2.961824183

Simplifying
z = -2.961824183

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.274324183, -2.961824183}
Solution
z = {0.274324183, -2.961824183}