5(6.2+z)z=3.8

Solution for 5(6.2+z)z=3.8 equation:

Simplifying
5(6.2 + z) * z = 3.8

Reorder the terms for easier multiplication:
5z(6.2 + z) = 3.8
(6.2 * 5z + z * 5z) = 3.8
(31z + 5z2) = 3.8

Solving
31z + 5z2 = 3.8

Solving for variable 'z'.

Reorder the terms:
-3.8 + 31z + 5z2 = 3.8 + -3.8

Combine like terms: 3.8 + -3.8 = 0.0
-3.8 + 31z + 5z2 = 0.0

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

Divide each side by '5'.
-0.76 + 6.2z + z2 = 0.0

Move the constant term to the right:

Add '0.76' to each side of the equation.
-0.76 + 6.2z + 0.76 + z2 = 0.0 + 0.76

Reorder the terms:
-0.76 + 0.76 + 6.2z + z2 = 0.0 + 0.76

Combine like terms: -0.76 + 0.76 = 0.00
0.00 + 6.2z + z2 = 0.0 + 0.76
6.2z + z2 = 0.0 + 0.76

Combine like terms: 0.0 + 0.76 = 0.76
6.2z + z2 = 0.76

The z term is 6.2z.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2z + 9.61 + z2 = 0.76 + 9.61

Reorder the terms:
9.61 + 6.2z + z2 = 0.76 + 9.61

Combine like terms: 0.76 + 9.61 = 10.37
9.61 + 6.2z + z2 = 10.37

Factor a perfect square on the left side:
(z + 3.1)(z + 3.1) = 10.37

Calculate the square root of the right side: 3.220248438

Break this problem into two subproblems by setting 
(z + 3.1) equal to 3.220248438 and -3.220248438.

Subproblem 1
z + 3.1 = 3.220248438

Simplifying
z + 3.1 = 3.220248438

Reorder the terms:
3.1 + z = 3.220248438

Solving
3.1 + z = 3.220248438

Solving for variable 'z'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + z = 3.220248438 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + z = 3.220248438 + -3.1
z = 3.220248438 + -3.1

Combine like terms: 3.220248438 + -3.1 = 0.120248438
z = 0.120248438

Simplifying
z = 0.120248438

Subproblem 2
z + 3.1 = -3.220248438

Simplifying
z + 3.1 = -3.220248438

Reorder the terms:
3.1 + z = -3.220248438

Solving
3.1 + z = -3.220248438

Solving for variable 'z'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + z = -3.220248438 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + z = -3.220248438 + -3.1
z = -3.220248438 + -3.1

Combine like terms: -3.220248438 + -3.1 = -6.320248438
z = -6.320248438

Simplifying
z = -6.320248438

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.120248438, -6.320248438}