Simplifying
(2m + 1)(2m + 1) = 4m + 2
Reorder the terms:
(1 + 2m)(2m + 1) = 4m + 2
Reorder the terms:
(1 + 2m)(1 + 2m) = 4m + 2
Multiply (1 + 2m) * (1 + 2m)
(1(1 + 2m) + 2m * (1 + 2m)) = 4m + 2
((1 * 1 + 2m * 1) + 2m * (1 + 2m)) = 4m + 2
((1 + 2m) + 2m * (1 + 2m)) = 4m + 2
(1 + 2m + (1 * 2m + 2m * 2m)) = 4m + 2
(1 + 2m + (2m + 4m^{2})) = 4m + 2
Combine like terms: 2m + 2m = 4m
(1 + 4m + 4m^{2}) = 4m + 2
Reorder the terms:
1 + 4m + 4m^{2} = 2 + 4m
Add '-4m' to each side of the equation.
1 + 4m + -4m + 4m^{2} = 2 + 4m + -4m
Combine like terms: 4m + -4m = 0
1 + 0 + 4m^{2} = 2 + 4m + -4m
1 + 4m^{2} = 2 + 4m + -4m
Combine like terms: 4m + -4m = 0
1 + 4m^{2} = 2 + 0
1 + 4m^{2} = 2
Solving
1 + 4m^{2} = 2
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 4m^{2} = 2 + -1
Combine like terms: 1 + -1 = 0
0 + 4m^{2} = 2 + -1
4m^{2} = 2 + -1
Combine like terms: 2 + -1 = 1
4m^{2} = 1
Divide each side by '4'.
m^{2} = 0.25
Simplifying
m^{2} = 0.25
Reorder the terms:
-0.25 + m^{2} = 0.25 + -0.25
Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + m^{2} = 0.00
Factor a difference between two squares.
(0.5 + m)(-0.5 + m) = 0.00
#### Subproblem 1

Set the factor '(0.5 + m)' equal to zero and attempt to solve:
Simplifying
0.5 + m = 0
Solving
0.5 + m = 0
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 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0 + -0.5
m = 0 + -0.5
Combine like terms: 0 + -0.5 = -0.5
m = -0.5
Simplifying
m = -0.5
#### Subproblem 2

Set the factor '(-0.5 + m)' equal to zero and attempt to solve:
Simplifying
-0.5 + m = 0
Solving
-0.5 + m = 0
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 + 0.5
Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 0 + 0.5
m = 0 + 0.5
Combine like terms: 0 + 0.5 = 0.5
m = 0.5
Simplifying
m = 0.5#### Solution

m = {-0.5, 0.5}