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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 + 4m2)) = 4m + 2

Combine like terms: 2m + 2m = 4m
(1 + 4m + 4m2) = 4m + 2

Reorder the terms:
1 + 4m + 4m2 = 2 + 4m

Add '-4m' to each side of the equation.
1 + 4m + -4m + 4m2 = 2 + 4m + -4m

Combine like terms: 4m + -4m = 0
1 + 0 + 4m2 = 2 + 4m + -4m
1 + 4m2 = 2 + 4m + -4m

Combine like terms: 4m + -4m = 0
1 + 4m2 = 2 + 0
1 + 4m2 = 2

Solving
1 + 4m2 = 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 + 4m2 = 2 + -1

Combine like terms: 1 + -1 = 0
0 + 4m2 = 2 + -1
4m2 = 2 + -1

Combine like terms: 2 + -1 = 1
4m2 = 1

Divide each side by '4'.
m2 = 0.25

Simplifying
m2 = 0.25

Reorder the terms:
-0.25 + m2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + m2 = 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}
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