4v^2+2=-9v

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Solution for 4v^2+2=-9v equation:


Simplifying
4v2 + 2 = -9v

Reorder the terms:
2 + 4v2 = -9v

Solving
2 + 4v2 = -9v

Solving for variable 'v'.

Reorder the terms:
2 + 9v + 4v2 = -9v + 9v

Combine like terms: -9v + 9v = 0
2 + 9v + 4v2 = 0

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

Subproblem 1

Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 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 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2

Subproblem 2

Set the factor '(1 + 4v)' equal to zero and attempt to solve: Simplifying 1 + 4v = 0 Solving 1 + 4v = 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 + 4v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4v = 0 + -1 4v = 0 + -1 Combine like terms: 0 + -1 = -1 4v = -1 Divide each side by '4'. v = -0.25 Simplifying v = -0.25

Solution

v = {-2, -0.25}

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