16m^2=16m+3

Solution for 16m^2=16m+3 equation:

Simplifying
16m2 = 16m + 3

Reorder the terms:
16m2 = 3 + 16m

Solving
16m2 = 3 + 16m

Solving for variable 'm'.

Reorder the terms:
-3 + -16m + 16m2 = 3 + 16m + -3 + -16m

Reorder the terms:
-3 + -16m + 16m2 = 3 + -3 + 16m + -16m

Combine like terms: 3 + -3 = 0
-3 + -16m + 16m2 = 0 + 16m + -16m
-3 + -16m + 16m2 = 16m + -16m

Combine like terms: 16m + -16m = 0
-3 + -16m + 16m2 = 0

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

Divide each side by '16'.
-0.1875 + -1m + m2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -1m + 0.1875 + m2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -1m + m2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -1m + m2 = 0 + 0.1875
-1m + m2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-1m + m2 = 0.1875

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 0.1875 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 0.1875 + 0.25

Combine like terms: 0.1875 + 0.25 = 0.4375
0.25 + -1m + m2 = 0.4375

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(m + -0.5) equal to 0.661437828 and -0.661437828.

Subproblem 1
m + -0.5 = 0.661437828

Simplifying
m + -0.5 = 0.661437828

Reorder the terms:
-0.5 + m = 0.661437828

Solving
-0.5 + m = 0.661437828

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 0.661437828 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 0.661437828 + 0.5
m = 0.661437828 + 0.5

Combine like terms: 0.661437828 + 0.5 = 1.161437828
m = 1.161437828

Simplifying
m = 1.161437828

Subproblem 2
m + -0.5 = -0.661437828

Simplifying
m + -0.5 = -0.661437828

Reorder the terms:
-0.5 + m = -0.661437828

Solving
-0.5 + m = -0.661437828

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -0.661437828 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -0.661437828 + 0.5
m = -0.661437828 + 0.5

Combine like terms: -0.661437828 + 0.5 = -0.161437828
m = -0.161437828

Simplifying
m = -0.161437828

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.161437828, -0.161437828}