4v^2+v=3

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Solution for 4v^2+v=3 equation:


Simplifying
4v2 + v = 3

Reorder the terms:
v + 4v2 = 3

Solving
v + 4v2 = 3

Solving for variable 'v'.

Reorder the terms:
-3 + v + 4v2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + v + 4v2 = 0

Factor a trinomial.
(-1 + -1v)(3 + -4v) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -4v)' equal to zero and attempt to solve: Simplifying 3 + -4v = 0 Solving 3 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4v = 0 + -3 -4v = 0 + -3 Combine like terms: 0 + -3 = -3 -4v = -3 Divide each side by '-4'. v = 0.75 Simplifying v = 0.75

Solution

v = {-1, 0.75}

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