(4z+3)(3z)=132

Solution for (4z+3)(3z)=132 equation:

Simplifying
(4z + 3)(3z) = 132

Reorder the terms:
(3 + 4z)(3z) = 132

Remove parenthesis around (3z)
(3 + 4z) * 3z = 132

Reorder the terms for easier multiplication:
3z(3 + 4z) = 132
(3 * 3z + 4z * 3z) = 132
(9z + 12z2) = 132

Solving
9z + 12z2 = 132

Solving for variable 'z'.

Reorder the terms:
-132 + 9z + 12z2 = 132 + -132

Combine like terms: 132 + -132 = 0
-132 + 9z + 12z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-44 + 3z + 4z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-44 + 3z + 4z2)' equal to zero and attempt to solve:

Simplifying
-44 + 3z + 4z2 = 0

Solving
-44 + 3z + 4z2 = 0

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

Divide each side by '4'.
-11 + 0.75z + z2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 0.75z + 11 + z2 = 0 + 11

Reorder the terms:
-11 + 11 + 0.75z + z2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 0.75z + z2 = 0 + 11
0.75z + z2 = 0 + 11

Combine like terms: 0 + 11 = 11
0.75z + z2 = 11

The z term is 0.75z.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75z + 0.140625 + z2 = 11 + 0.140625

Reorder the terms:
0.140625 + 0.75z + z2 = 11 + 0.140625

Combine like terms: 11 + 0.140625 = 11.140625
0.140625 + 0.75z + z2 = 11.140625

Factor a perfect square on the left side:
(z + 0.375)(z + 0.375) = 11.140625

Calculate the square root of the right side: 3.337757481

Break this problem into two subproblems by setting 
(z + 0.375) equal to 3.337757481 and -3.337757481.

Subproblem 1
z + 0.375 = 3.337757481

Simplifying
z + 0.375 = 3.337757481

Reorder the terms:
0.375 + z = 3.337757481

Solving
0.375 + z = 3.337757481

Solving for variable 'z'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + z = 3.337757481 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + z = 3.337757481 + -0.375
z = 3.337757481 + -0.375

Combine like terms: 3.337757481 + -0.375 = 2.962757481
z = 2.962757481

Simplifying
z = 2.962757481

Subproblem 2
z + 0.375 = -3.337757481

Simplifying
z + 0.375 = -3.337757481

Reorder the terms:
0.375 + z = -3.337757481

Solving
0.375 + z = -3.337757481

Solving for variable 'z'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + z = -3.337757481 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + z = -3.337757481 + -0.375
z = -3.337757481 + -0.375

Combine like terms: -3.337757481 + -0.375 = -3.712757481
z = -3.712757481

Simplifying
z = -3.712757481

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.962757481, -3.712757481}
Solution
z = {2.962757481, -3.712757481}