(1-v)(2v-9)=0

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Solution for (1-v)(2v-9)=0 equation:


Simplifying
(1 + -1v)(2v + -9) = 0

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

Multiply (1 + -1v) * (-9 + 2v)
(1(-9 + 2v) + -1v * (-9 + 2v)) = 0
((-9 * 1 + 2v * 1) + -1v * (-9 + 2v)) = 0
((-9 + 2v) + -1v * (-9 + 2v)) = 0
(-9 + 2v + (-9 * -1v + 2v * -1v)) = 0
(-9 + 2v + (9v + -2v2)) = 0

Combine like terms: 2v + 9v = 11v
(-9 + 11v + -2v2) = 0

Solving
-9 + 11v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-9 + 2v)(1 + -1v) = 0

Subproblem 1

Set the factor '(-9 + 2v)' equal to zero and attempt to solve: Simplifying -9 + 2v = 0 Solving -9 + 2v = 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 + 2v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2v = 0 + 9 2v = 0 + 9 Combine like terms: 0 + 9 = 9 2v = 9 Divide each side by '2'. v = 4.5 Simplifying v = 4.5

Subproblem 2

Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1

Solution

v = {4.5, 1}

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