10v^2-16=-8v^2-39v+8

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Solution for 10v^2-16=-8v^2-39v+8 equation:


Simplifying
10v2 + -16 = -8v2 + -39v + 8

Reorder the terms:
-16 + 10v2 = -8v2 + -39v + 8

Reorder the terms:
-16 + 10v2 = 8 + -39v + -8v2

Solving
-16 + 10v2 = 8 + -39v + -8v2

Solving for variable 'v'.

Reorder the terms:
-16 + -8 + 39v + 10v2 + 8v2 = 8 + -39v + -8v2 + -8 + 39v + 8v2

Combine like terms: -16 + -8 = -24
-24 + 39v + 10v2 + 8v2 = 8 + -39v + -8v2 + -8 + 39v + 8v2

Combine like terms: 10v2 + 8v2 = 18v2
-24 + 39v + 18v2 = 8 + -39v + -8v2 + -8 + 39v + 8v2

Reorder the terms:
-24 + 39v + 18v2 = 8 + -8 + -39v + 39v + -8v2 + 8v2

Combine like terms: 8 + -8 = 0
-24 + 39v + 18v2 = 0 + -39v + 39v + -8v2 + 8v2
-24 + 39v + 18v2 = -39v + 39v + -8v2 + 8v2

Combine like terms: -39v + 39v = 0
-24 + 39v + 18v2 = 0 + -8v2 + 8v2
-24 + 39v + 18v2 = -8v2 + 8v2

Combine like terms: -8v2 + 8v2 = 0
-24 + 39v + 18v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 13v + 6v2) = 0

Factor a trinomial.
3((-8 + -3v)(1 + -2v)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-8 + -3v)' equal to zero and attempt to solve: Simplifying -8 + -3v = 0 Solving -8 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3v = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3v = 0 + 8 -3v = 0 + 8 Combine like terms: 0 + 8 = 8 -3v = 8 Divide each side by '-3'. v = -2.666666667 Simplifying v = -2.666666667

Subproblem 2

Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5

Solution

v = {-2.666666667, 0.5}

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