4v^7+18v^6-10v^5=0

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Solution for 4v^7+18v^6-10v^5=0 equation:


Simplifying
4v7 + 18v6 + -10v5 = 0

Reorder the terms:
-10v5 + 18v6 + 4v7 = 0

Solving
-10v5 + 18v6 + 4v7 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2v5'.
2v5(-5 + 9v + 2v2) = 0

Factor a trinomial.
2v5((-5 + -1v)(1 + -2v)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'v5' equal to zero and attempt to solve: Simplifying v5 = 0 Solving v5 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

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

Subproblem 3

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 = {-5, 0.5}

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