(2-u)(3u-5)=0

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Solution for (2-u)(3u-5)=0 equation:


Simplifying
(2 + -1u)(3u + -5) = 0

Reorder the terms:
(2 + -1u)(-5 + 3u) = 0

Multiply (2 + -1u) * (-5 + 3u)
(2(-5 + 3u) + -1u * (-5 + 3u)) = 0
((-5 * 2 + 3u * 2) + -1u * (-5 + 3u)) = 0
((-10 + 6u) + -1u * (-5 + 3u)) = 0
(-10 + 6u + (-5 * -1u + 3u * -1u)) = 0
(-10 + 6u + (5u + -3u2)) = 0

Combine like terms: 6u + 5u = 11u
(-10 + 11u + -3u2) = 0

Solving
-10 + 11u + -3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + u)(5 + -3u) = 0

Subproblem 1

Set the factor '(-2 + u)' equal to zero and attempt to solve: Simplifying -2 + u = 0 Solving -2 + u = 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 + u = 0 + 2 Combine like terms: -2 + 2 = 0 0 + u = 0 + 2 u = 0 + 2 Combine like terms: 0 + 2 = 2 u = 2 Simplifying u = 2

Subproblem 2

Set the factor '(5 + -3u)' equal to zero and attempt to solve: Simplifying 5 + -3u = 0 Solving 5 + -3u = 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 + -3u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3u = 0 + -5 -3u = 0 + -5 Combine like terms: 0 + -5 = -5 -3u = -5 Divide each side by '-3'. u = 1.666666667 Simplifying u = 1.666666667

Solution

u = {2, 1.666666667}

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