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Simplifying U3 = 14U2 + 32U Reorder the terms: U3 = 32U + 14U2 Solving U3 = 32U + 14U2 Solving for variable 'U'. Reorder the terms: -32U + -14U2 + U3 = 32U + 14U2 + -32U + -14U2 Reorder the terms: -32U + -14U2 + U3 = 32U + -32U + 14U2 + -14U2 Combine like terms: 32U + -32U = 0 -32U + -14U2 + U3 = 0 + 14U2 + -14U2 -32U + -14U2 + U3 = 14U2 + -14U2 Combine like terms: 14U2 + -14U2 = 0 -32U + -14U2 + U3 = 0 Factor out the Greatest Common Factor (GCF), 'U'. U(-32 + -14U + U2) = 0 Factor a trinomial. U((-2 + -1U)(16 + -1U)) = 0Subproblem 1
Set the factor 'U' equal to zero and attempt to solve: Simplifying U = 0 Solving U = 0 Move all terms containing U to the left, all other terms to the right. Simplifying U = 0Subproblem 2
Set the factor '(-2 + -1U)' equal to zero and attempt to solve: Simplifying -2 + -1U = 0 Solving -2 + -1U = 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 + -1U = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1U = 0 + 2 -1U = 0 + 2 Combine like terms: 0 + 2 = 2 -1U = 2 Divide each side by '-1'. U = -2 Simplifying U = -2Subproblem 3
Set the factor '(16 + -1U)' equal to zero and attempt to solve: Simplifying 16 + -1U = 0 Solving 16 + -1U = 0 Move all terms containing U to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1U = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1U = 0 + -16 -1U = 0 + -16 Combine like terms: 0 + -16 = -16 -1U = -16 Divide each side by '-1'. U = 16 Simplifying U = 16Solution
U = {0, -2, 16}
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