3v^2+7v=6

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Solution for 3v^2+7v=6 equation:


Simplifying
3v2 + 7v = 6

Reorder the terms:
7v + 3v2 = 6

Solving
7v + 3v2 = 6

Solving for variable 'v'.

Reorder the terms:
-6 + 7v + 3v2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 7v + 3v2 = 0

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

Subproblem 1

Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3

Subproblem 2

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

Solution

v = {-3, 0.6666666667}

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