3v^2+6v-103=2

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Solution for 3v^2+6v-103=2 equation:


Simplifying
3v2 + 6v + -103 = 2

Reorder the terms:
-103 + 6v + 3v2 = 2

Solving
-103 + 6v + 3v2 = 2

Solving for variable 'v'.

Reorder the terms:
-103 + -2 + 6v + 3v2 = 2 + -2

Combine like terms: -103 + -2 = -105
-105 + 6v + 3v2 = 2 + -2

Combine like terms: 2 + -2 = 0
-105 + 6v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 2v + v2) = 0

Factor a trinomial.
3((-7 + -1v)(5 + -1v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 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 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7

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 = {-7, 5}

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