4u^4v^2+4u^2v+1=0

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Solution for 4u^4v^2+4u^2v+1=0 equation:


Simplifying
4u4v2 + 4u2v + 1 = 0

Reorder the terms:
1 + 4u2v + 4u4v2 = 0

Solving
1 + 4u2v + 4u4v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(1 + 2u2v)(1 + 2u2v) = 0

Subproblem 1

Set the factor '(1 + 2u2v)' equal to zero and attempt to solve: Simplifying 1 + 2u2v = 0 Solving 1 + 2u2v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2u2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2u2v = 0 + -1 2u2v = 0 + -1 Combine like terms: 0 + -1 = -1 2u2v = -1 Divide each side by '2v'. u2 = -0.5v-1 Simplifying u2 = -0.5v-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + 2u2v)' equal to zero and attempt to solve: Simplifying 1 + 2u2v = 0 Solving 1 + 2u2v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2u2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2u2v = 0 + -1 2u2v = 0 + -1 Combine like terms: 0 + -1 = -1 2u2v = -1 Divide each side by '2v'. u2 = -0.5v-1 Simplifying u2 = -0.5v-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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