3v^2-9v=30

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Solution for 3v^2-9v=30 equation:


Simplifying
3v2 + -9v = 30

Reorder the terms:
-9v + 3v2 = 30

Solving
-9v + 3v2 = 30

Solving for variable 'v'.

Reorder the terms:
-30 + -9v + 3v2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -9v + 3v2 = 0

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

Factor a trinomial.
3((-2 + -1v)(5 + -1v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 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 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2

Subproblem 2

Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5

Solution

v = {-2, 5}

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