(2u-3)(7-u)=0

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Solution for (2u-3)(7-u)=0 equation:


Simplifying
(2u + -3)(7 + -1u) = 0

Reorder the terms:
(-3 + 2u)(7 + -1u) = 0

Multiply (-3 + 2u) * (7 + -1u)
(-3(7 + -1u) + 2u * (7 + -1u)) = 0
((7 * -3 + -1u * -3) + 2u * (7 + -1u)) = 0
((-21 + 3u) + 2u * (7 + -1u)) = 0
(-21 + 3u + (7 * 2u + -1u * 2u)) = 0
(-21 + 3u + (14u + -2u2)) = 0

Combine like terms: 3u + 14u = 17u
(-21 + 17u + -2u2) = 0

Solving
-21 + 17u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + u)(3 + -2u) = 0

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 = 7

Subproblem 2

Set the factor '(3 + -2u)' equal to zero and attempt to solve: Simplifying 3 + -2u = 0 Solving 3 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2u = 0 + -3 -2u = 0 + -3 Combine like terms: 0 + -3 = -3 -2u = -3 Divide each side by '-2'. u = 1.5 Simplifying u = 1.5

Solution

u = {7, 1.5}

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