(1-v)(3v-7)=0

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Solution for (1-v)(3v-7)=0 equation:


Simplifying
(1 + -1v)(3v + -7) = 0

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

Multiply (1 + -1v) * (-7 + 3v)
(1(-7 + 3v) + -1v * (-7 + 3v)) = 0
((-7 * 1 + 3v * 1) + -1v * (-7 + 3v)) = 0
((-7 + 3v) + -1v * (-7 + 3v)) = 0
(-7 + 3v + (-7 * -1v + 3v * -1v)) = 0
(-7 + 3v + (7v + -3v2)) = 0

Combine like terms: 3v + 7v = 10v
(-7 + 10v + -3v2) = 0

Solving
-7 + 10v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + 3v)(1 + -1v) = 0

Subproblem 1

Set the factor '(-7 + 3v)' equal to zero and attempt to solve: Simplifying -7 + 3v = 0 Solving -7 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 3v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3v = 0 + 7 3v = 0 + 7 Combine like terms: 0 + 7 = 7 3v = 7 Divide each side by '3'. v = 2.333333333 Simplifying v = 2.333333333

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 = {2.333333333, 1}

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