3v(3v^2+4v-7)=0

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Solution for 3v(3v^2+4v-7)=0 equation:


Simplifying
3v(3v2 + 4v + -7) = 0

Reorder the terms:
3v(-7 + 4v + 3v2) = 0
(-7 * 3v + 4v * 3v + 3v2 * 3v) = 0
(-21v + 12v2 + 9v3) = 0

Solving
-21v + 12v2 + 9v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(-7 + 4v + 3v2) = 0

Factor a trinomial.
3v((-7 + -3v)(1 + -1v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0

Subproblem 2

Set the factor '(-7 + -3v)' equal to zero and attempt to solve: Simplifying -7 + -3v = 0 Solving -7 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3v = 0 + 7 -3v = 0 + 7 Combine like terms: 0 + 7 = 7 -3v = 7 Divide each side by '-3'. v = -2.333333333 Simplifying v = -2.333333333

Subproblem 3

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 = {0, -2.333333333, 1}

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