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Simplifying (2 + u)(4u + -9) = 0 Reorder the terms: (2 + u)(-9 + 4u) = 0 Multiply (2 + u) * (-9 + 4u) (2(-9 + 4u) + u(-9 + 4u)) = 0 ((-9 * 2 + 4u * 2) + u(-9 + 4u)) = 0 ((-18 + 8u) + u(-9 + 4u)) = 0 (-18 + 8u + (-9 * u + 4u * u)) = 0 (-18 + 8u + (-9u + 4u2)) = 0 Combine like terms: 8u + -9u = -1u (-18 + -1u + 4u2) = 0 Solving -18 + -1u + 4u2 = 0 Solving for variable 'u'. Factor a trinomial. (-2 + -1u)(9 + -4u) = 0Subproblem 1
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 2
Set the factor '(9 + -4u)' equal to zero and attempt to solve: Simplifying 9 + -4u = 0 Solving 9 + -4u = 0 Move all terms containing u to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4u = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4u = 0 + -9 -4u = 0 + -9 Combine like terms: 0 + -9 = -9 -4u = -9 Divide each side by '-4'. u = 2.25 Simplifying u = 2.25Solution
u = {-2, 2.25}
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