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Simplifying u2 + -4 = 2u2 + 2u + -3 Reorder the terms: -4 + u2 = 2u2 + 2u + -3 Reorder the terms: -4 + u2 = -3 + 2u + 2u2 Solving -4 + u2 = -3 + 2u + 2u2 Solving for variable 'u'. Reorder the terms: -4 + 3 + -2u + u2 + -2u2 = -3 + 2u + 2u2 + 3 + -2u + -2u2 Combine like terms: -4 + 3 = -1 -1 + -2u + u2 + -2u2 = -3 + 2u + 2u2 + 3 + -2u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -1 + -2u + -1u2 = -3 + 2u + 2u2 + 3 + -2u + -2u2 Reorder the terms: -1 + -2u + -1u2 = -3 + 3 + 2u + -2u + 2u2 + -2u2 Combine like terms: -3 + 3 = 0 -1 + -2u + -1u2 = 0 + 2u + -2u + 2u2 + -2u2 -1 + -2u + -1u2 = 2u + -2u + 2u2 + -2u2 Combine like terms: 2u + -2u = 0 -1 + -2u + -1u2 = 0 + 2u2 + -2u2 -1 + -2u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -1 + -2u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2u + u2) = 0 Factor a trinomial. -1((1 + u)(1 + u)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + u)' equal to zero and attempt to solve: Simplifying 1 + u = 0 Solving 1 + u = 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 + u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u = 0 + -1 u = 0 + -1 Combine like terms: 0 + -1 = -1 u = -1 Simplifying u = -1Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve: Simplifying 1 + u = 0 Solving 1 + u = 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 + u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u = 0 + -1 u = 0 + -1 Combine like terms: 0 + -1 = -1 u = -1 Simplifying u = -1Solution
u = {-1, -1}
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