54.3=(930+51m)(16+m)

Solution for 54.3=(930+51m)(16+m) equation:

Simplifying
54.3 = (930 + 51m)(16 + m)

Multiply (930 + 51m) * (16 + m)
54.3 = (930(16 + m) + 51m * (16 + m))
54.3 = ((16 * 930 + m * 930) + 51m * (16 + m))
54.3 = ((14880 + 930m) + 51m * (16 + m))
54.3 = (14880 + 930m + (16 * 51m + m * 51m))
54.3 = (14880 + 930m + (816m + 51m2))

Combine like terms: 930m + 816m = 1746m
54.3 = (14880 + 1746m + 51m2)

Solving
54.3 = 14880 + 1746m + 51m2

Solving for variable 'm'.

Combine like terms: 54.3 + -14880 = -14825.7
-14825.7 + -1746m + -51m2 = 14880 + 1746m + 51m2 + -14880 + -1746m + -51m2

Reorder the terms:
-14825.7 + -1746m + -51m2 = 14880 + -14880 + 1746m + -1746m + 51m2 + -51m2

Combine like terms: 14880 + -14880 = 0
-14825.7 + -1746m + -51m2 = 0 + 1746m + -1746m + 51m2 + -51m2
-14825.7 + -1746m + -51m2 = 1746m + -1746m + 51m2 + -51m2

Combine like terms: 1746m + -1746m = 0
-14825.7 + -1746m + -51m2 = 0 + 51m2 + -51m2
-14825.7 + -1746m + -51m2 = 51m2 + -51m2

Combine like terms: 51m2 + -51m2 = 0
-14825.7 + -1746m + -51m2 = 0

Begin completing the square.  Divide all terms by
-51 the coefficient of the squared term: 

Divide each side by '-51'.
290.7 + 34.23529412m + m2 = 0

Move the constant term to the right:

Add '-290.7' to each side of the equation.
290.7 + 34.23529412m + -290.7 + m2 = 0 + -290.7

Reorder the terms:
290.7 + -290.7 + 34.23529412m + m2 = 0 + -290.7

Combine like terms: 290.7 + -290.7 = 0.0
0.0 + 34.23529412m + m2 = 0 + -290.7
34.23529412m + m2 = 0 + -290.7

Combine like terms: 0 + -290.7 = -290.7
34.23529412m + m2 = -290.7

The m term is 34.23529412m.  Take half its coefficient (17.11764706).
Square it (293.0138409) and add it to both sides.

Add '293.0138409' to each side of the equation.
34.23529412m + 293.0138409 + m2 = -290.7 + 293.0138409

Reorder the terms:
293.0138409 + 34.23529412m + m2 = -290.7 + 293.0138409

Combine like terms: -290.7 + 293.0138409 = 2.3138409
293.0138409 + 34.23529412m + m2 = 2.3138409

Factor a perfect square on the left side:
(m + 17.11764706)(m + 17.11764706) = 2.3138409

Calculate the square root of the right side: 1.521131454

Break this problem into two subproblems by setting 
(m + 17.11764706) equal to 1.521131454 and -1.521131454.

Subproblem 1
m + 17.11764706 = 1.521131454

Simplifying
m + 17.11764706 = 1.521131454

Reorder the terms:
17.11764706 + m = 1.521131454

Solving
17.11764706 + m = 1.521131454

Solving for variable 'm'.

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

Add '-17.11764706' to each side of the equation.
17.11764706 + -17.11764706 + m = 1.521131454 + -17.11764706

Combine like terms: 17.11764706 + -17.11764706 = 0.00000000
0.00000000 + m = 1.521131454 + -17.11764706
m = 1.521131454 + -17.11764706

Combine like terms: 1.521131454 + -17.11764706 = -15.596515606
m = -15.596515606

Simplifying
m = -15.596515606

Subproblem 2
m + 17.11764706 = -1.521131454

Simplifying
m + 17.11764706 = -1.521131454

Reorder the terms:
17.11764706 + m = -1.521131454

Solving
17.11764706 + m = -1.521131454

Solving for variable 'm'.

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

Add '-17.11764706' to each side of the equation.
17.11764706 + -17.11764706 + m = -1.521131454 + -17.11764706

Combine like terms: 17.11764706 + -17.11764706 = 0.00000000
0.00000000 + m = -1.521131454 + -17.11764706
m = -1.521131454 + -17.11764706

Combine like terms: -1.521131454 + -17.11764706 = -18.638778514
m = -18.638778514

Simplifying
m = -18.638778514

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-15.596515606, -18.638778514}