20m^4=5m^2

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Solution for 20m^4=5m^2 equation:


Simplifying
20m4 = 5m2

Solving
20m4 = 5m2

Solving for variable 'm'.

Reorder the terms:
-5m2 + 20m4 = 5m2 + -5m2

Combine like terms: 5m2 + -5m2 = 0
-5m2 + 20m4 = 0

Factor out the Greatest Common Factor (GCF), '5m2'.
5m2(-1 + 4m2) = 0

Factor a difference between two squares.
5m2((1 + 2m)(-1 + 2m)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}

Subproblem 2

Set the factor '(1 + 2m)' equal to zero and attempt to solve: Simplifying 1 + 2m = 0 Solving 1 + 2m = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2m = 0 + -1 2m = 0 + -1 Combine like terms: 0 + -1 = -1 2m = -1 Divide each side by '2'. m = -0.5 Simplifying m = -0.5

Subproblem 3

Set the factor '(-1 + 2m)' equal to zero and attempt to solve: Simplifying -1 + 2m = 0 Solving -1 + 2m = 0 Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2m = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2m = 0 + 1 2m = 0 + 1 Combine like terms: 0 + 1 = 1 2m = 1 Divide each side by '2'. m = 0.5 Simplifying m = 0.5

Solution

m = {0, -0.5, 0.5}

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