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

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Solution for (7-v)(2v-1)=0 equation:


Simplifying
(7 + -1v)(2v + -1) = 0

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

Multiply (7 + -1v) * (-1 + 2v)
(7(-1 + 2v) + -1v * (-1 + 2v)) = 0
((-1 * 7 + 2v * 7) + -1v * (-1 + 2v)) = 0
((-7 + 14v) + -1v * (-1 + 2v)) = 0
(-7 + 14v + (-1 * -1v + 2v * -1v)) = 0
(-7 + 14v + (1v + -2v2)) = 0

Combine like terms: 14v + 1v = 15v
(-7 + 15v + -2v2) = 0

Solving
-7 + 15v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + v)(1 + -2v) = 0

Subproblem 1

Set the factor '(-7 + v)' equal to zero and attempt to solve: Simplifying -7 + v = 0 Solving -7 + v = 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 + v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + v = 0 + 7 v = 0 + 7 Combine like terms: 0 + 7 = 7 v = 7 Simplifying v = 7

Subproblem 2

Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5

Solution

v = {7, 0.5}

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