(4v-5)(9-v)=0

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Solution for (4v-5)(9-v)=0 equation:


Simplifying
(4v + -5)(9 + -1v) = 0

Reorder the terms:
(-5 + 4v)(9 + -1v) = 0

Multiply (-5 + 4v) * (9 + -1v)
(-5(9 + -1v) + 4v * (9 + -1v)) = 0
((9 * -5 + -1v * -5) + 4v * (9 + -1v)) = 0
((-45 + 5v) + 4v * (9 + -1v)) = 0
(-45 + 5v + (9 * 4v + -1v * 4v)) = 0
(-45 + 5v + (36v + -4v2)) = 0

Combine like terms: 5v + 36v = 41v
(-45 + 41v + -4v2) = 0

Solving
-45 + 41v + -4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-9 + v)(5 + -4v) = 0

Subproblem 1

Set the factor '(-9 + v)' equal to zero and attempt to solve: Simplifying -9 + v = 0 Solving -9 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + v = 0 + 9 v = 0 + 9 Combine like terms: 0 + 9 = 9 v = 9 Simplifying v = 9

Subproblem 2

Set the factor '(5 + -4v)' equal to zero and attempt to solve: Simplifying 5 + -4v = 0 Solving 5 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4v = 0 + -5 -4v = 0 + -5 Combine like terms: 0 + -5 = -5 -4v = -5 Divide each side by '-4'. v = 1.25 Simplifying v = 1.25

Solution

v = {9, 1.25}

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