3v^2-v=14

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Solution for 3v^2-v=14 equation:


Simplifying
3v2 + -1v = 14

Reorder the terms:
-1v + 3v2 = 14

Solving
-1v + 3v2 = 14

Solving for variable 'v'.

Reorder the terms:
-14 + -1v + 3v2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -1v + 3v2 = 0

Factor a trinomial.
(-2 + -1v)(7 + -3v) = 0

Subproblem 1

Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2

Subproblem 2

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

Solution

v = {-2, 2.333333333}

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