9v^2=24+30v

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Solution for 9v^2=24+30v equation:


Simplifying
9v2 = 24 + 30v

Solving
9v2 = 24 + 30v

Solving for variable 'v'.

Reorder the terms:
-24 + -30v + 9v2 = 24 + 30v + -24 + -30v

Reorder the terms:
-24 + -30v + 9v2 = 24 + -24 + 30v + -30v

Combine like terms: 24 + -24 = 0
-24 + -30v + 9v2 = 0 + 30v + -30v
-24 + -30v + 9v2 = 30v + -30v

Combine like terms: 30v + -30v = 0
-24 + -30v + 9v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -10v + 3v2) = 0

Factor a trinomial.
3((-2 + -3v)(4 + -1v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -3v)' equal to zero and attempt to solve: Simplifying -2 + -3v = 0 Solving -2 + -3v = 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 + -3v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3v = 0 + 2 -3v = 0 + 2 Combine like terms: 0 + 2 = 2 -3v = 2 Divide each side by '-3'. v = -0.6666666667 Simplifying v = -0.6666666667

Subproblem 2

Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4

Solution

v = {-0.6666666667, 4}

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