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Simplifying u4v3 + -81v3 = 0 Solving u4v3 + -81v3 = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '81v3' to each side of the equation. u4v3 + -81v3 + 81v3 = 0 + 81v3 Combine like terms: -81v3 + 81v3 = 0 u4v3 + 0 = 0 + 81v3 u4v3 = 0 + 81v3 Remove the zero: u4v3 = 81v3 Divide each side by 'v3'. u4 = 81 Simplifying u4 = 81 Reorder the terms: -81 + u4 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + u4 = 0 Factor a difference between two squares. (9 + u2)(-9 + u2) = 0 Factor a difference between two squares. (9 + u2)((3 + u)(-3 + u)) = 0Subproblem 1
Set the factor '(9 + u2)' equal to zero and attempt to solve: Simplifying 9 + u2 = 0 Solving 9 + u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + u2 = 0 + -9 u2 = 0 + -9 Combine like terms: 0 + -9 = -9 u2 = -9 Simplifying u2 = -9 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 '(3 + u)' equal to zero and attempt to solve: Simplifying 3 + u = 0 Solving 3 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + u = 0 + -3 u = 0 + -3 Combine like terms: 0 + -3 = -3 u = -3 Simplifying u = -3Subproblem 3
Set the factor '(-3 + u)' equal to zero and attempt to solve: Simplifying -3 + u = 0 Solving -3 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 0 + 3 Combine like terms: -3 + 3 = 0 0 + u = 0 + 3 u = 0 + 3 Combine like terms: 0 + 3 = 3 u = 3 Simplifying u = 3Solution
u = {-3, 3}
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