3v^2-6=-3v

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Solution for 3v^2-6=-3v equation:


Simplifying
3v2 + -6 = -3v

Reorder the terms:
-6 + 3v2 = -3v

Solving
-6 + 3v2 = -3v

Solving for variable 'v'.

Reorder the terms:
-6 + 3v + 3v2 = -3v + 3v

Combine like terms: -3v + 3v = 0
-6 + 3v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + v + v2) = 0

Factor a trinomial.
3((-2 + -1v)(1 + -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 '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 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 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1

Solution

v = {-2, 1}

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