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Simplifying (4u + -2)(7 + u) = 0 Reorder the terms: (-2 + 4u)(7 + u) = 0 Multiply (-2 + 4u) * (7 + u) (-2(7 + u) + 4u * (7 + u)) = 0 ((7 * -2 + u * -2) + 4u * (7 + u)) = 0 ((-14 + -2u) + 4u * (7 + u)) = 0 (-14 + -2u + (7 * 4u + u * 4u)) = 0 (-14 + -2u + (28u + 4u2)) = 0 Combine like terms: -2u + 28u = 26u (-14 + 26u + 4u2) = 0 Solving -14 + 26u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 13u + 2u2) = 0 Factor a trinomial. 2((-7 + -1u)(1 + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve: Simplifying -7 + -1u = 0 Solving -7 + -1u = 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 + -1u = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1u = 0 + 7 -1u = 0 + 7 Combine like terms: 0 + 7 = 7 -1u = 7 Divide each side by '-1'. 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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