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Simplifying (7 + -1u)(4u + -2) = 0 Reorder the terms: (7 + -1u)(-2 + 4u) = 0 Multiply (7 + -1u) * (-2 + 4u) (7(-2 + 4u) + -1u * (-2 + 4u)) = 0 ((-2 * 7 + 4u * 7) + -1u * (-2 + 4u)) = 0 ((-14 + 28u) + -1u * (-2 + 4u)) = 0 (-14 + 28u + (-2 * -1u + 4u * -1u)) = 0 (-14 + 28u + (2u + -4u2)) = 0 Combine like terms: 28u + 2u = 30u (-14 + 30u + -4u2) = 0 Solving -14 + 30u + -4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 15u + -2u2) = 0 Factor a trinomial. 2((-7 + u)(1 + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + u)' equal to zero and attempt to solve: Simplifying -7 + u = 0 Solving -7 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = 0 + 7 Combine like terms: -7 + 7 = 0 0 + u = 0 + 7 u = 0 + 7 Combine like terms: 0 + 7 = 7 u = 7 Simplifying u = 7Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve: Simplifying 1 + -2u = 0 Solving 1 + -2u = 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 + -2u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u = 0 + -1 -2u = 0 + -1 Combine like terms: 0 + -1 = -1 -2u = -1 Divide each side by '-2'. u = 0.5 Simplifying u = 0.5Solution
u = {7, 0.5}
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