(2u-5)(9-u)=0

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Solution for (2u-5)(9-u)=0 equation:


Simplifying
(2u + -5)(9 + -1u) = 0

Reorder the terms:
(-5 + 2u)(9 + -1u) = 0

Multiply (-5 + 2u) * (9 + -1u)
(-5(9 + -1u) + 2u * (9 + -1u)) = 0
((9 * -5 + -1u * -5) + 2u * (9 + -1u)) = 0
((-45 + 5u) + 2u * (9 + -1u)) = 0
(-45 + 5u + (9 * 2u + -1u * 2u)) = 0
(-45 + 5u + (18u + -2u2)) = 0

Combine like terms: 5u + 18u = 23u
(-45 + 23u + -2u2) = 0

Solving
-45 + 23u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + u)(5 + -2u) = 0

Subproblem 1

Set the factor '(-9 + u)' equal to zero and attempt to solve: Simplifying -9 + u = 0 Solving -9 + u = 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 + u = 0 + 9 Combine like terms: -9 + 9 = 0 0 + u = 0 + 9 u = 0 + 9 Combine like terms: 0 + 9 = 9 u = 9 Simplifying u = 9

Subproblem 2

Set the factor '(5 + -2u)' equal to zero and attempt to solve: Simplifying 5 + -2u = 0 Solving 5 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2u = 0 + -5 -2u = 0 + -5 Combine like terms: 0 + -5 = -5 -2u = -5 Divide each side by '-2'. u = 2.5 Simplifying u = 2.5

Solution

u = {9, 2.5}

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