3v^2=198+15v

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Solution for 3v^2=198+15v equation:


Simplifying
3v2 = 198 + 15v

Solving
3v2 = 198 + 15v

Solving for variable 'v'.

Reorder the terms:
-198 + -15v + 3v2 = 198 + 15v + -198 + -15v

Reorder the terms:
-198 + -15v + 3v2 = 198 + -198 + 15v + -15v

Combine like terms: 198 + -198 = 0
-198 + -15v + 3v2 = 0 + 15v + -15v
-198 + -15v + 3v2 = 15v + -15v

Combine like terms: 15v + -15v = 0
-198 + -15v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-66 + -5v + v2) = 0

Factor a trinomial.
3((-6 + -1v)(11 + -1v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-6 + -1v)' equal to zero and attempt to solve: Simplifying -6 + -1v = 0 Solving -6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1v = 0 + 6 -1v = 0 + 6 Combine like terms: 0 + 6 = 6 -1v = 6 Divide each side by '-1'. v = -6 Simplifying v = -6

Subproblem 2

Set the factor '(11 + -1v)' equal to zero and attempt to solve: Simplifying 11 + -1v = 0 Solving 11 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1v = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1v = 0 + -11 -1v = 0 + -11 Combine like terms: 0 + -11 = -11 -1v = -11 Divide each side by '-1'. v = 11 Simplifying v = 11

Solution

v = {-6, 11}

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