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Simplifying u(x + 2) * u(-1x + 2) = 0 Reorder the terms: u(2 + x) * u(-1x + 2) = 0 Reorder the terms: u(2 + x) * u(2 + -1x) = 0 Reorder the terms for easier multiplication: u * u(2 + x)(2 + -1x) = 0 Multiply u * u u2(2 + x)(2 + -1x) = 0 Multiply (2 + x) * (2 + -1x) u2(2(2 + -1x) + x(2 + -1x)) = 0 u2((2 * 2 + -1x * 2) + x(2 + -1x)) = 0 u2((4 + -2x) + x(2 + -1x)) = 0 u2(4 + -2x + (2 * x + -1x * x)) = 0 u2(4 + -2x + (2x + -1x2)) = 0 Combine like terms: -2x + 2x = 0 u2(4 + 0 + -1x2) = 0 u2(4 + -1x2) = 0 (4 * u2 + -1x2 * u2) = 0 (4u2 + -1u2x2) = 0 Solving 4u2 + -1u2x2 = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'u2'. u2(4 + -1x2) = 0 Factor a difference between two squares. u2((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve: Simplifying u2 = 0 Solving u2 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u2 = 0 Take the square root of each side: u = {0}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
u = {0}
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