9v^2+12vf+4f^2=0

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Solution for 9v^2+12vf+4f^2=0 equation:


Simplifying
9v2 + 12vf + 4f2 = 0

Reorder the terms:
12fv + 4f2 + 9v2 = 0

Solving
12fv + 4f2 + 9v2 = 0

Solving for variable 'f'.

Factor a trinomial.
(2f + 3v)(2f + 3v) = 0

Subproblem 1

Set the factor '(2f + 3v)' equal to zero and attempt to solve: Simplifying 2f + 3v = 0 Solving 2f + 3v = 0 Move all terms containing f to the left, all other terms to the right. Add '-3v' to each side of the equation. 2f + 3v + -3v = 0 + -3v Combine like terms: 3v + -3v = 0 2f + 0 = 0 + -3v 2f = 0 + -3v Remove the zero: 2f = -3v Divide each side by '2'. f = -1.5v Simplifying f = -1.5v

Subproblem 2

Set the factor '(2f + 3v)' equal to zero and attempt to solve: Simplifying 2f + 3v = 0 Solving 2f + 3v = 0 Move all terms containing f to the left, all other terms to the right. Add '-3v' to each side of the equation. 2f + 3v + -3v = 0 + -3v Combine like terms: 3v + -3v = 0 2f + 0 = 0 + -3v 2f = 0 + -3v Remove the zero: 2f = -3v Divide each side by '2'. f = -1.5v Simplifying f = -1.5v

Solution

f = {-1.5v, -1.5v}

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