(3v^5+8v^3-10v^2)-(-12v^5+4v^3+14v^2)=0

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Solution for (3v^5+8v^3-10v^2)-(-12v^5+4v^3+14v^2)=0 equation:


Simplifying
(3v5 + 8v3 + -10v2) + -1(-12v5 + 4v3 + 14v2) = 0

Reorder the terms:
(-10v2 + 8v3 + 3v5) + -1(-12v5 + 4v3 + 14v2) = 0

Remove parenthesis around (-10v2 + 8v3 + 3v5)
-10v2 + 8v3 + 3v5 + -1(-12v5 + 4v3 + 14v2) = 0

Reorder the terms:
-10v2 + 8v3 + 3v5 + -1(14v2 + 4v3 + -12v5) = 0
-10v2 + 8v3 + 3v5 + (14v2 * -1 + 4v3 * -1 + -12v5 * -1) = 0
-10v2 + 8v3 + 3v5 + (-14v2 + -4v3 + 12v5) = 0

Reorder the terms:
-10v2 + -14v2 + 8v3 + -4v3 + 3v5 + 12v5 = 0

Combine like terms: -10v2 + -14v2 = -24v2
-24v2 + 8v3 + -4v3 + 3v5 + 12v5 = 0

Combine like terms: 8v3 + -4v3 = 4v3
-24v2 + 4v3 + 3v5 + 12v5 = 0

Combine like terms: 3v5 + 12v5 = 15v5
-24v2 + 4v3 + 15v5 = 0

Solving
-24v2 + 4v3 + 15v5 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), 'v2'.
v2(-24 + 4v + 15v3) = 0

Subproblem 1

Set the factor 'v2' equal to zero and attempt to solve: Simplifying v2 = 0 Solving v2 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v2 = 0 Take the square root of each side: v = {0}

Subproblem 2

Set the factor '(-24 + 4v + 15v3)' equal to zero and attempt to solve: Simplifying -24 + 4v + 15v3 = 0 Solving -24 + 4v + 15v3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

v = {0}

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