84=(5m+1)(m+1)

Solution for 84=(5m+1)(m+1) equation:

Simplifying
84 = (5m + 1)(m + 1)

Reorder the terms:
84 = (1 + 5m)(m + 1)

Reorder the terms:
84 = (1 + 5m)(1 + m)

Multiply (1 + 5m) * (1 + m)
84 = (1(1 + m) + 5m * (1 + m))
84 = ((1 * 1 + m * 1) + 5m * (1 + m))
84 = ((1 + 1m) + 5m * (1 + m))
84 = (1 + 1m + (1 * 5m + m * 5m))
84 = (1 + 1m + (5m + 5m2))

Combine like terms: 1m + 5m = 6m
84 = (1 + 6m + 5m2)

Solving
84 = 1 + 6m + 5m2

Solving for variable 'm'.

Combine like terms: 84 + -1 = 83
83 + -6m + -5m2 = 1 + 6m + 5m2 + -1 + -6m + -5m2

Reorder the terms:
83 + -6m + -5m2 = 1 + -1 + 6m + -6m + 5m2 + -5m2

Combine like terms: 1 + -1 = 0
83 + -6m + -5m2 = 0 + 6m + -6m + 5m2 + -5m2
83 + -6m + -5m2 = 6m + -6m + 5m2 + -5m2

Combine like terms: 6m + -6m = 0
83 + -6m + -5m2 = 0 + 5m2 + -5m2
83 + -6m + -5m2 = 5m2 + -5m2

Combine like terms: 5m2 + -5m2 = 0
83 + -6m + -5m2 = 0

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

Divide each side by '-5'.
-16.6 + 1.2m + m2 = 0

Move the constant term to the right:

Add '16.6' to each side of the equation.
-16.6 + 1.2m + 16.6 + m2 = 0 + 16.6

Reorder the terms:
-16.6 + 16.6 + 1.2m + m2 = 0 + 16.6

Combine like terms: -16.6 + 16.6 = 0.0
0.0 + 1.2m + m2 = 0 + 16.6
1.2m + m2 = 0 + 16.6

Combine like terms: 0 + 16.6 = 16.6
1.2m + m2 = 16.6

The m term is 1.2m.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2m + 0.36 + m2 = 16.6 + 0.36

Reorder the terms:
0.36 + 1.2m + m2 = 16.6 + 0.36

Combine like terms: 16.6 + 0.36 = 16.96
0.36 + 1.2m + m2 = 16.96

Factor a perfect square on the left side:
(m + 0.6)(m + 0.6) = 16.96

Calculate the square root of the right side: 4.118252056

Break this problem into two subproblems by setting 
(m + 0.6) equal to 4.118252056 and -4.118252056.

Subproblem 1
m + 0.6 = 4.118252056

Simplifying
m + 0.6 = 4.118252056

Reorder the terms:
0.6 + m = 4.118252056

Solving
0.6 + m = 4.118252056

Solving for variable 'm'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + m = 4.118252056 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + m = 4.118252056 + -0.6
m = 4.118252056 + -0.6

Combine like terms: 4.118252056 + -0.6 = 3.518252056
m = 3.518252056

Simplifying
m = 3.518252056

Subproblem 2
m + 0.6 = -4.118252056

Simplifying
m + 0.6 = -4.118252056

Reorder the terms:
0.6 + m = -4.118252056

Solving
0.6 + m = -4.118252056

Solving for variable 'm'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + m = -4.118252056 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + m = -4.118252056 + -0.6
m = -4.118252056 + -0.6

Combine like terms: -4.118252056 + -0.6 = -4.718252056
m = -4.718252056

Simplifying
m = -4.718252056

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.518252056, -4.718252056}