(5z+4)(3+z)=4

Solution for (5z+4)(3+z)=4 equation:

Simplifying
(5z + 4)(3 + z) = 4

Reorder the terms:
(4 + 5z)(3 + z) = 4

Multiply (4 + 5z) * (3 + z)
(4(3 + z) + 5z * (3 + z)) = 4
((3 * 4 + z * 4) + 5z * (3 + z)) = 4
((12 + 4z) + 5z * (3 + z)) = 4
(12 + 4z + (3 * 5z + z * 5z)) = 4
(12 + 4z + (15z + 5z2)) = 4

Combine like terms: 4z + 15z = 19z
(12 + 19z + 5z2) = 4

Solving
12 + 19z + 5z2 = 4

Solving for variable 'z'.

Reorder the terms:
12 + -4 + 19z + 5z2 = 4 + -4

Combine like terms: 12 + -4 = 8
8 + 19z + 5z2 = 4 + -4

Combine like terms: 4 + -4 = 0
8 + 19z + 5z2 = 0

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

Divide each side by '5'.
1.6 + 3.8z + z2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 3.8z + -1.6 + z2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 3.8z + z2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 3.8z + z2 = 0 + -1.6
3.8z + z2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
3.8z + z2 = -1.6

The z term is 3.8z.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8z + 3.61 + z2 = -1.6 + 3.61

Reorder the terms:
3.61 + 3.8z + z2 = -1.6 + 3.61

Combine like terms: -1.6 + 3.61 = 2.01
3.61 + 3.8z + z2 = 2.01

Factor a perfect square on the left side:
(z + 1.9)(z + 1.9) = 2.01

Calculate the square root of the right side: 1.417744688

Break this problem into two subproblems by setting 
(z + 1.9) equal to 1.417744688 and -1.417744688.

Subproblem 1
z + 1.9 = 1.417744688

Simplifying
z + 1.9 = 1.417744688

Reorder the terms:
1.9 + z = 1.417744688

Solving
1.9 + z = 1.417744688

Solving for variable 'z'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + z = 1.417744688 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + z = 1.417744688 + -1.9
z = 1.417744688 + -1.9

Combine like terms: 1.417744688 + -1.9 = -0.482255312
z = -0.482255312

Simplifying
z = -0.482255312

Subproblem 2
z + 1.9 = -1.417744688

Simplifying
z + 1.9 = -1.417744688

Reorder the terms:
1.9 + z = -1.417744688

Solving
1.9 + z = -1.417744688

Solving for variable 'z'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + z = -1.417744688 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + z = -1.417744688 + -1.9
z = -1.417744688 + -1.9

Combine like terms: -1.417744688 + -1.9 = -3.317744688
z = -3.317744688

Simplifying
z = -3.317744688

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.482255312, -3.317744688}